When an E-4 calls me "hey" or "hey man" knowing that I am an officer, should I bother to correct him?

Oh HELL YES. That kind of casual informality is totally off base. If he knows you are an officer he is to show you the same respect in or out of uniform. Not sure if saluting is required in civies but the proper respect needs to be recognized.

This is one of those where the answer is going to depend on the two of you are when it occurs.
As a general hard rule if the person knows you are an officer and the two of you meet in civvies, let's say at the Commissary BX/PX etc... yes, he should refer to you as sir. And this standard should apply regardless of where you are in the US.

Now... the rules change when you step outside of the US. Even though we have bases, posts, ports all over the world we still have to maintain OPSEC and that means changing some customs when off post and out of uniform. The haircuts usually give us away but it should be permissible to use the more familiar when out and about in foreign countries. That said that only goes so far.

Of course, you have to be upset. Any enlisted or lower-ranking officers must respect the Chain of Command. In my Team, I was the lowest-enlisted TM, we were a Unique Team/Family. Lots of respect was honored. I gained respect from my superiors that we treated each 0ther with the soul, my CSM Green Beret all his life over 40 years, never called me SP4 Velez, instead he would call me Pee (brother). I loved my job and missions with Col. Weekley, Cpt. Baggley, Lt. Rendethorson, CW4 Smith, Maj. Diaz. I wish I could find them and have a cookout.

It has always been Sir or Rank. NO EXCEPTIONS was what we were Taught in BASIC. So my question is, where did this Soldier go to BASIC at and who didn't inform him of this Common Curtesy? This Young Man needs some reminding. Push the ground till I'M Tired. I still say we need to go back to Basic like it was in the 70's. So in common curtesy i would stop him and REIND him one time and when he does it again Stop and Drop.. Maybe he will Learn.

Rank is rank, wherever you are.

Dear Captain R. You should bring the SPC to one side and have a brief conversation to him telling him that he needs to be respectful to those who holds the officers rank from a WO up to a General. Ask the individual, if roles were reverse and that if he was an officer, how would he feel if someone called him "hey man or what's up man"? You worked hard to get the rank, and others should respect your rank office which you hold...He might realize his mistake, and going on might be respectful.

not sure what you mean "outside of work"
but I was taught that you as a captain, ask who the soldiers platoon sargent is, company and unit commander...then you let that company commander know what happened, who the soldier was and who the platoon sargent is, then they correct him, because it is their failure and they need to know about it
officers converse with officers out of the chain of command, they dont deal directly with enlisted that are not in their chain of command

so if you were a colonel you would address the colonel of that command

it could be setup to where you are in at a meeting with all involved to find out what the issue actually is...perhaps the whole unit does the same thing, in that case you have found a weak link command and at the top level it needs addressed...maybe a general needs to know about it

I have been involved with something like this...once when I was a fledgling e-4....it never works to the soldiers and the units benefit if you correct them and no one else knows about it...because they will continue to not meet the standard
I like SFC Casey O'Mally answer, but I felt it needed elaborated

The correct greeting, with respect, should be "hello sir" nothing more, nothing less. The way the military has gone these days is way to soft in my opinion. Honor, courage, commitment, respect need to be the standard not just some words that are passed around.

If wearing civilian clothes, identify yourself.
Describe the behavior.
Describe the policy.
Never Argue. Never apologize.
Follow up and ensure the correction is made.

This former E-5 turned officer says, yes, you correct him.