How to put in contacts without getting wrinkles?

I have heard that you're really not supposed to pull down your eye when you're applying eyeliner to your bottom waterline because you'll get wrinkles. so I don't do that, but you have to pull down your eye to put in contacts. I'm worried cause I'm starting to get wrinkles under my eyes and my under-eye circles are bad. Is this normal? Should I be putting in contacts differently?