I started a birth control pill and had to switch to a new one only a week after being on my other one. will my period still start at the same time?

Generally speaking,: Your new BC pill will determine the onset of your next period. If you started on day 1 of a 28 day pack in which the last 7 pills are "blanks" or sugar pills, your period should "reset" to that last week as determined by the new pill pack. Remember that you may not be consistent for a few months after starting birth control or changing formulations. So the answer is "no," your period will reset.