Yes, that's normal. Different Corns can behave very differently in identical setups. Sounds like your first one preferred to hide away until it was used to the new home, whilst this one is more interested in trying to find a way out. Don't worry - this behaviour should calm down over the next week or two. As usual with new arrivals, the trick is to minimise stress as far as possible by not handling or feeding for at least a week.
I don't believe that any diseases or parasites can pass between cats and reptiles. Your main concern is that the cat can't get to the snakes and the snakes can't get out to the cat. Some determined cats have been known to "break in" to screen lids, so if you have one, make sure that the cat can't get up there and sit on it. Cats do seem fascinated by the way that snakes move.
However, the presence of the cat may be disturbing the new arrival even more, so it might be a good idea to keep the cat out of the room for a few days whilst your new arrival is settling. If you can't do that, then perhaps put newspapers around the tank so that the cat can't see in. In the long term it shouldn't be a problem once the snake is settled in. My cat and snakes used to follow each other up and down the glass front of the vivs - the snakes seemed as interested in her as she was in them!