What does it mean to go "up and over" the slurs as opposed to going "down into" them? Does it mean playing one hand unslurred while you play the other hand slurred, as opposed to using the pedal when either hand is playing a slurred passage and therefore slurring both? Or maybe you're referring to the type of hand movement...
Is your new teacher able to tell you why a certain technique (way of moving) is better than another?Why don't you ask and let us know how it went?
...or, if you can't get an explaination, just give your new teacher the benefit of the doubt and try it that way, if you don't like the outcome you don't have to keep it, but you might be missing out. At least, you'll have picked up a different trick for your bag.
Shoot them both and teach yourself !! ONLY KIDDING