It would make no sense if it was 'the same frog'. None at all.
Quite the opposite. It would make no sense if it wasn't. You're not being smart enough about this.
All the Scratch did was change the point in time the kids and guardians got sent to Earth. That's all. In other words, history changed from about 1930 when Jade and John arrived instead of Jake and Jane. The first obvious change is that since John wasn't carrying flintlock pistols, Sassacre didn't get shot. And obviously through the butterfly effect everything changed from there on.
If the Alpha universe was in a different location... where the heck would that be? Did a new, pre-won Incipisphere just pop into being with a new frog in it? Of course not. The Alpha universe was reset, but it's still the universe the trolls created and it's still getting destroyed by Jack.