Play to the whistle, not the AR's flag, right?
This. The AR merely indicates that he feels like an offside offence occurs, the decision rests solely on the referee though.
Best example would be the first of Nathan Burns' hattrick goals. Flag went up because Burns was in an offside position when ball was played, but it was kicked by Paartalu so no offence occured. Would be rubbish if the referee had just blindly followed the AR's flag.