The times shown on the jam's home page are local time. If you're using a computer with a mouse and hover over the closing time, it will show you the time in UTC. It doesn't matter whether you use local time or UTC, so long as you submit your entry before that closing time and make it public so that it is visible to everyone as soon as submissions close. The only unknown factor here is how long before submissions close is acceptable to make it public. This is just my opinion, but I think 24 hours before the submission deadline is reasonable to account for people living in different time zones.
Whatever you do, don't leave it until the last minute in case you have internet issues. I had internet troubles one time and ended up submitting just minutes after the deadline. Fortunately for me, the deadline had been extended and I didn't realise it.