Subsequent semi-diurnal (twice daily) tides happen precisely once every 12 hours and 25 minutes. given what you know of the motions of the earth and moon, where is this extra 25 minutes likely coming from?

The time required for the moon to orbit around the earth is slightly longer than the earth rotation on its axis. The moon rotates in the same direction that the earth rotates on its axis. Thus, the moon's full rotation requires another 50min or 25 minutes per crossing of the earth's meridian.