Do I have to synchronize the Time manually? What do I do if the PC time is different from the eBay time?

No, you shouldn't have to synchronize the time by hand at any point.

JBidwatcher synchronizes it's view of the time every 30-40 minutes, including the time difference between your system clock and the eBay clock in its adjustment to what your computer's clock says it is.

It tries very hard to line itself up with eBay's time, even if your clock is not synched up with eBay's clock.