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

If we have to handle such a simple correction as this with kid gloves, we have gone too soft. What does the Major think a squad leader should do if one of his/her Soldiers is standing out in the open in a firefight? Should he/she politely ask the Soldier to take cover?
I can't imagine what basic is like anymore. "Now, Soldiers, it's 10 AM and we have a lot to do. Please, put your phones away and get out of bed."

Well done. You were correct to call the PFC on military courtesy. It is not aggressive.
I notice you are a SPC. Since neither of the O's said anything, it was not your responsibility.
They were, I'm guessing, medical types and probably were baffled by the BS and frightened when you corrected someone without apologizing to the offender first for correcting her.
NEXT
You do what is correct and salute when appropriate.
Leave the ass chewing to the one / group the offense was against.
Apparently, the Major and LT do not think they have earned the PFCs respect, although their rank is entitled to a salute. One salutes the rank not the wearer.

As a retired USAF First Sergeant I probably would have been more aggressive than the SPC. It doesn't matter which service you are in or the officers are in - YOU SALUTE. I would have been looking for his supervisor to provide remedial training.

Hmm, bit passive aggressive for me. Thank you for the corrective action.

Hey boot, didn’t you learn how to salute in boot camp?

I was always taught "Praise in public, correct in private", so it would be best to call aside and correct her in private, face to face.

But you were spot on! Get in their butt, it won't happen again.

They just need a couple of days of extra duty practicing.

At the same time, though, if I have one aggravation about saluting it's this: The 'Officer Head Dip Salute.' A proper salute is rendered with the upper arm parallel to the ground and the fingertips meeting the eyebrow and the cap visor. It bothers me even today in my retired, enlisted state when I see an officer raise his hand part way to a proper salute and dip his brow to reach his fingertips. Sir or Ma'am, it's a two way street. If I render a salute, please return with a proper, buy-the-book, military salute!

as an NCO in the Marine Corps, i was taught to pull the junior grade to the side, instruct them on proper saluting of officers etiquette and send them on their way. i do not see any problem in in the SPC asking the PFC the question, the PFC made a mistake . how is the aggressive?