IMO, I think you were correct. Warning an assistant is just a way to tell him to shut up. Wanting to whack a kid for having his shirt out sounds like someone read a new rule this week and didn't understand the whole thing.
My warning for shirts not tucked in comes in pregame. I will give a courtesy warning during a FT - "Check your shirts guys". If someone gives me any kind of an attitude or refuses to tuck them in neatly, I ask them to follow me and send them out. If you take care of it early - 1st qtr - you won't have to worry about it any more during the game. I am a jerk about this issue. (If there's a circumstance that's odd, I take that into consideration - i.e. older uni's that have short tails, etc.)
About the assistant coach - I do not talk to assistant coaches - period. I sit them down immediately when they stand up for any reason (other than to spontaneously cheer for a play) and if they address me, that's my reply - I don't talk to assistants. If they get pi$$y, I let the coach know they need to control them or I will.