Are you paid by the hour? Any job I've ever had with such rigid time tracking requirements was a hourly paid position.

This sort of thing backfires on the employer in my opinion. It's quite easy to stretch a task to fill 8 hours if you have to be there anyway. But maybe you'd be happy to clock out after 5 hours one day and take a few extra unpaid hours for yourself. If your work is done, the employer should be happy to save a little money and let you do that.