I really hope that you will be keeping the cat indoors at night too. For his/her safety as much as anything else.
My cat used to belong to my next door neighbours until they abandoned him. He was outside all the time until I started keeping him inside my home at night. I got sick of taking him to the vets - because I knew they wouldn't - to have him patched up after fights with possums and other cats. He has had near misses with cars and had another neighbour kick at him repeatedly. Please keep the cat safe!
The comment you made about Buckley would worry me. In saying that, your own can be different to other peoples animals. Batty will play with, wrestle with & chase and be chased by Bobby but it is all on Bobby's terms. He starts the games and finishes them and while Batty will play he doesn't instigate the games. That rule has been very well reinforced since Batty was 9 weeks old though.