When is your first night in the Turin hotel booked? ie for the night you arrive, or not until the night after?
Have you checked if public transport is available at that time? Just because it's crap in most of the UK, doesn't mean it is everywhere, it could be that there are trains 24/7 between Milan and Turin - I was once panicking about a late arrival at Malta airport for a holiday in Gozo, which is a ferry ride away, but when I checked, there was a ferry every 90 mins all night, so a bit of a wait, but totally fine.
Otherwise, a hotel at your arrival airport sounds like a plan. You could check in, sleep, get up, have breakfast and even see a bit of Milan before your onward journey to Turin.
But yes, something to be aware of, city break 'packages' are almost always 'flight + hotel' rather than transfer included. Usually because you just get public transport from the airport, so no need for an organised transfer.