For a 12 period moving average, that average is based on the period I am displaying, correct?

For example, if I am displaying 30 minute intervals, then my moving average is based on the quotes at the end of the 30 minutes. If I am displaying daily intervals, my moving average is based on quotes at the end of the day.

Yes, it counts 12 bars back; that would be the bars it has in the history, which may have holes, so it's not necessarily 12*Period or evenly distributed time-wise. In particular, early each week, the 12 bars reaches back to late the week before.