First of all treats -- what flavor of wet or dry food is he eating? If it's chicken, then try chicken treats. It's possible he never was given treats in his other home and cats don't actually need treats. They are just that -- a treat. If he doesn't want them, don't force them on him (although most cats LOVE treats).
As for the doggy door. At some point, Rocky will find it. Just recently we started letting an outdoor cat inside and it didn't take long for him to find the cat door to the outdoor enclosure. My bengal took a while to figure out how to open it as he used to use his paw instead of his head.
A lot depends on where this doggy door leads. To the open outdoors? To a fenced in yard? Will Rocky go exploring if he gets outside? Are you planning on allowing him access outside? There are pet doors that can be activated only by a microchip, so it would be set for your dog and not Rocky. Rocky could not get out.
Once a cat is outside, it needs to start making its territory! That includes rubbing his cheek up against anything and maybe even spraying (marking). Even if he is neutered, male cats can still spray. Many people simply let their cats outside. Others supervise them. Others harness and leash them and take them on walks. It's a personal decision.
So much depends on your particular area, the size of your yard, etc. Busy streets are a problem for cats -- traffic, people. Your biggest worry may be someone stealing a beautiful bengal. It happens. The best thing is to keep your kitty inside and safe or outside with supervision or controlled with a leash.
Interestingly enough, you mentioned that in Rocky's previous home, he beat up a dog. How is he getting along with your dog?
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