After going back in time and the cinematic you'll be in Hill Valley's town square. Answer the questions any way you like and you'll be able to continue on your way.
Walk to the police station, not that you can get the "Hi, Bob" Trophy
Go past the police station to the windows with bars on it. Speak with Doc Brown for a first time until the police officer comes out of the police station. Now talk to Doc Brown a second time.
The trophy pops!