Sounds about right having to push the pistons all the way in when you done new pads & discs.
I had to when i did the rear ones. Even when i did just front pads i had to push pistons in all way to get the pads to fit.
Shouldnt bind tho ? are they just touching so when you spin the wheel you can hear them slipping against each other or are they binding so much its hard to spin the wheel ?
Check your brake fluid level, it may be a bit high now you have winded the pistons back in.