What’s the proper way to correct someone when not saluting an officer?

What you did (correct a junior enlisted soldier) was correct. Perhaps the proper challenge to the PFC would have been, "you just passed two officers, plus you need to be more aware of your surroundings. If you had been, you would have seen them and rendered the proper greeting of the day and a hand salute." With that said, the PFC should have complied with your correction and then carried on. Regardless of what the Major felt, you should have mentioned to him/her, in a private setting, proper military protocol, and then left it at that. Obviously, said Major is probably not familiar with Army tradition and used to a more laid back or sedimentary atmosphere. A little more education from you might help fix the problem.

It's kinda of a two-way street. I was a 1LT and walking with another LT on our hospital compound in Korea. A Captain (doctor) stopped us and asked we didn't salute him. I told him when he started acting like an officer, he would be treated like one and he was standing in the street out of uniform.
No response from him, so we left with no salute rendered.
Smartass on my part and could have caused trouble, but he started shaping up.
This was before the movie "MASH" came out and some of our doctors and nurses could have been tactical advisors for Hawkeye and Hot Lips.

blinded from eye wound.

I've seen two schools of thought playout in situations such as this:
1. Pull the enlisted SM aside and remind them of customs & courtesies.
2. Jump on them and smoke the customs & courtesies back into them.

What's best? Depends I suppose. Know your audience and take your pick.

You did the right thing.

I got lit up for this once, I was coming out of medical. I just woke up, and was sent back to the barrack’s. I couldn’t see, think,walk. But I sure got chewed, then they got me some help

A failure to Salute MUST be addressed on the spot! The Officer MUST be provided Military Respect for their rank. I would have locked the PFC's heels and no matter what another officer's response was! You, as an Officer Must require the show of respect by those serving in the Military regardless of which branch of service that are a part of. ;-) I SALUTE All My Fellow Veterans!!!

Like a first class petty officer corrected me when I was an E2..... "Hey! Are you stupid? Even I have to salute that guy!"

Counsel the miscreant on what violation of ART 89 UCMJ will earn him/her.

Yes do ask politely the pfc that you would appreciate a moment and take the pfc aside,know which standard you are referring to and remind 5he pfc of this for future reference. Should your c.o. witness you not leading, it might cost you, career wise later. It's a tradition you don't uphold I'm the field but on duty at least on post you do. Many officers have earned the respect and many enlisted men have carried on the time honored greeting of respect.

I believe the comments was appropriate. When stationed at Fort Knox we had many long convoys with rank displayed on the vehicles. On the way to my lab/office an E1 faked to salute vehicles with ranks up to O.7. I was tired but saluted as appropriate . When the convoy passed I called to the rainee. He came as called, asked why no salute.. I asked his name and unit and walked off to the nearby hospital. After a few calls I called his unit and my call was tanferred up the chain of commandI reached he commanding officer who told me to meet him at the Officers Club at 1700 hrs. He looked surprised when a medical service officer with spit shined shoes and crisp khaki Uniforme showed up. He looked surprised and bought me a drink. He explained this trainee was a racial agitator and everyone else was fearful of repercussions. I assured him that was the least of my fears and he had his Sergeant Major meet me to sign the documents. He stated he would proceed with an Article 15 and it would likely be refused and aCourts Martial would follow. Much to our surprise tha “radical “. Trainee accepted the non judicial punishment. When I had enlisted I knew there would be times of fear, and you never let control you, you acted on-site of it. WaynePrice

Perfect answer. A lesson I learned years ago. Correct failures like this smartly and the kesson is learned.

Lastly, how you approach the SPC is important. Which should be carried out with the utmost professionalism and professional respect.

You were justified asking that Soldier why she didn’t salute and all service members should question such disrespect, even though at times it may be unintentional.

As a fairly new Army Reserve SPC assigned to a unit that drilled on a Navy base I was very skittish about saluting the wrong people. I knew my Army rank and how to quickly identify officers but trying to differentiate Navy officers from Senior Enlisted with the sun in your eyes, and all the different uniforms. I got yelled at by a Petty Officer for saluting him one day, the next day I apparently missed a Captain in a group of NCO's because one of them watched to see what building I entered, and I received a phone call from from him as I was standing at the front desk waiting for to pick up the keys I had been sent for. I stopped leaving the building on foot if at all possible after that when I was there during the week. (Changed into uniform after I got to work, went right out to "our" parking lot at lunch, changed before leaving at the end of the day.) A PFC may not have even been to basic yet if they are in the delayed entry program. Correct them yes, but try to avoid embarrassing them, shaming them does not help the learning process.
Eventually I did start leaving the building at lunch with some of the older junior officers and junior NCO's, they would give me a "heads up" or "you're good" when a bunch of navy in khaki was headed in our direction. Between that and volunteering with the Sea Cadets I now know Navy rank and uniforms, but as a new Specialist it was just one more thing some Sergeant to yell at you about. Officers don't usually bother to make the lives of Junior Enlisted soldiers miserable, (at least not intentionally).

No, you should point it out as humanly as possible. I remember a PFC getting reamed by an LT for not saluting him.

Major was wrong. You do have to be aggressive. You are in the military. The point of the military is to fight wars. Whatever you DO in the military is immaterial, you are all in support of war fighting. Remarks complete.

Protocol.... you need this to maintain the relationship between officers and enlisted.

You could have asked soldier if they noticed the officer's that she just past. Then again was you in a no solute area?

Praise in public, correct in private. It is one of the duties of leadership to teach juniors. One on one where possible is best

You weren't aggressive.
Aggressive: " Hey!! Sh*t for brains!! Did you not see these two SUPERIOR OFFICERS
(Capitalization denotes speaking at a perceived auditory decibel range akin to the noise level present at the detonation of a 10 kiloton nuclear warhead)!!
Now drop and shove the f*ckin' Earth off its normal orbital path until we are over your perceived horizon!!"

Non-Aggressive:
"Do enlisted soldiers not salute officers anymore?"

Pull the soldier off to the side and remind them of customs and courtesies. Holding the standard is what makes us military personnel and keeping that state of mind. The more you let lower personnel to lose their grip the worse it is going to get when eventually someone will say what is the big deal.

My first question would be WHAT THE FUCK IS YOUR MAJOR MALFUNCTION? You do realize that was two officers that passed you without you rendering the proper respect and saluting them? The only way I would say nothing is if it was an officer that passed. A PFC has no reason or right not to salute his/her superior officer.

There is no other way.

F that agressive BS. Drop the PFC for push ups and maybe put her on KP for about a week

Happened to me ages ago. I apologized for not saluting to the Commissioned Officer, while saluting. The E-7 that was with her asked if I was okay (I was on a pain pill that messed with my vision so badly I was looking at the ground). I said that was no excuse, and the E-7 said words to me I hear to this day: "Stay alert, stay alive soldier".

Should have just lit her ass up. Sometimes that's just what everyone needs.

I find the best way to start those conversations is with a "Hey Motherf***er" and go from there.

You were correct to calmly address the PFC.

Praise in public, correct in private.