Welcome to the Chalk Bucket and the world of Gymnastics!

To answer your question - "Is it normal?" I would say, no, it is not normal. However, it also isn't unheard of.
I don't usually give too much info about my DD, but I'll share a bit, hoping that it may help you some. DD started gym at 3.5. They were "amazed" at what she could do naturally and how quickly she picked up skills. She was CRAZY strong and CRAZY flexible. She picked up a lot of skills immediately and soon had her doing back walkovers, back hip circles, and front limbers. She and I both loved it, she for the gymnastics, and me because 1 - she loved it and I loved watching her and 2 - (ashamed to admit) I loved the fact that all the other parents oohed and aahed and told me she was going to the olympics. Boy was I naive.
Well, as soon as she turned 4, I switched her to a "better" gym. It was very frustrating for me at first because they had her working on things like handstands and cartwheels on the floor. I thought "the first gym had her working on her beam cartwheel and backhandsprings - what was wrong with these people." Well, the truth hit me (mostly from viewing things on the chalkbucket). SHE WAS 4!!!!! It had been totally inappropriate for the other gym to be working on those more advanced skills and not concentrating on basics. Perhaps if she'd stayed at the other gym she would be doing some amazing things right now, but then again, maybe she'd be in a back brace.
So, just a word of caution - You said this gym had your girls doing handstand bridge kick-overs. Perhaps it was not a coach showing them these things. Maybe it was just an older girl they were imitating. However, I would definitely keep an eye on things.
It does sound like your girls have a lot of natural ability and strength. The key at this age will be to keep it fun so that they stay in the sport and to focus on basics.
Once again, welcome and I wish you and your girls the best!