It happens with some planes more than others, mostly trainers with lots of dihedral but it can happen on others, too.

What I did with my Nexstar was to initiate the turn with ailerons, use the rudder to kick the tail around while simultaneously feeding in opposite aileron to correct for the coupling (what you are talking about is called coupling), and start to roll out of the turn. That plane had a ridiculous amount of dihedral. I don't think I've ever really needed 'opposite' aileron in a turn otherwise.

Flying a real cessna, there is a little coupling. Just requires less ailerons to make a turn.

Some people will mix ailerons to rudder to compensate, but I think it's best to learn how to handle a plane without mixes. Use mixes as tools, not crutches.