Sounds like they were just playing. If you keep letting him out, word of warning, he is going to want to go out more and more. Which is OK if you are alright with him eventually becoming an indoor/outdoor cat. I know that some people think it's cruel to leave a cat indoors all the time, and that it is best for them to be able to come and go. I think for some cats, that works out, but you always run the risk of them getting hit by a car, attacked by a dog or other animal. My cats are indoor, except for a feral that I care for, and she lives outside, always has, except she does sleep in the garage on cold nights.
I think your kitty was just playing with the neighbor cat. But you will have to worry about other cats that will not be so nice to him. Just be prepared, he may be ok with short visits out now, but he will eventually want to go out more and more, and you will not always be able to see his every move. Once they have a taste of the outdoor life, they will door dash at every opportunity they get.