Looking Out for Yourself
Regardless of what your contract might say - and especially if you don't have anything on paper - your actions during the first week or two on a new job will define how things are done in the future.
If you get sucked into working ten hours of unpaid overtime in the first week, because you want to show that you're an eager employee, you will have established that this is a normal practice, and will keep doing it pretty much forever.
If though, during that first week, when asked to donate time for unplanned work, you can beg off - "gee, if only you had told me earlier, my kid is having a heart transplant, and I'm assisting the surgeon, otherwise I would have been happy to do it," you will have established on some level that doing extra is an unusual situation.
Funny thing is, if you can consistently avoid extra, unpaid work, you'll find that they'll manage just fine, or that someone less clever will be given the work.
Timesheets are a GOOD thing, not because bosses insist on them, but because they force YOU to keep track of what you do.
Even if they're not required, it's very good practice to sit down at the end of each day and make notes about how your time was consumed.
It's good for you to actually think about these things, and it will make you a more productive employee. It also allows you to spot problems that might otherwise go unnoticed.
Best of all though, in the event that you and your employer wind up facing off behind lawyers you'll be very, very glad to have documented your work patterns and conditions.
Detailed notes and time sheets can save you if there's any dispute.
Which is why you not only fill out the damned time sheets, you make sure to take a copy off site, and store it at home.