I still don't see where the posessive comes in. I see John's action (kissing), but not his posession (John's kisses). I see his action here, and I see his action toward Jane.

What I think we have here is an irregular sentence structure that violates some of the normal rules. This structure is used to describe timing sensitive events. However, the structure is English, as it makes sense to most people. If you give most people your sentence, they would say that you were wrong. If it sounds wrong, that means it is wrong. (This is not always true, but the exceptions have to do with formal English, which is a slightly different beast than common English.)

I forgot to add, I come from the school of thought that says, "English is as it is spoken, and the rules of English describe this." If there is a conflict between the language and the rules, I always side with the language. If you were raised speaking English, you speak your native dialect correctly.