That would depend on your unit, some units have unwritten rules like that, but unless you are in a leadership position as a SPC then the answer is no. I would be up to your sqd ldr or team ldr to correct those privates.
You have to set ground rules with them. There's no regulations that states it but you have to let them know you don't operate like that. I know in combat arms units PVTs stand at parade rest for PV2s and PFCs. I would definitely go to my change of command with the issues.
It depends on your position. If you are a team leader or acting squad leader, then it would seem reasonable for you to administer corrective training. Talk with your first line NCO and platoon Sergeant and see what his/her take is on it. I'm not too keen on junior enlisted standing at parade rest for other junior enlisted regardless of rank or position, but when I was with the 82nd that was the how we conducted business. Regardless of rank, any Soldier can make an on the spot correction.