if you hit someone and they say its alright can they get you in trouble later on still...?
I was driving and I made a turn to other lane without looking and my back and hit the guys front end in back of me and left black strip on his but he said don't worry about it can they change there mind after and get you in trouble like next day?
Yeah, the can and will likely change their mind.
It's with in their right to do so.
Consider talking to your insurance company just in case.