The new contract starts the day the old one expires, yes. This is what I'm getting at. Strictly speaking he only has 5 months left on his current deal.
A rolling contract renews every second in theory. A 12 month rolling contract is just that, at any given time it has 12 months to run. According to the Cambridge dictionary a rolling contract runs until one party ends it as opposed to running to a fixed date. I would assume adding in 12 months ( or any other length of time ) is to do with compensation either way.