In that case, I would suggest to use one connection for one transaction. So essentially transaction can not be spanned across multiple sessions but certainly it can span across multiple requests.
It's possible you mean the right thing, but the wording as it is is not correct (or at the least highly misleading). Transactions really do not figure into this. The usual way to do this would be to maintain a DB connection pool for the web app, and then to obtain a connection from it if a request comes in that needs DB access. After the request is completed, the connection should be returned to the pool. Open connections should *not* be stored in sessions - you'd run out of connections pretty quickly.