For example, if you currently have a cookie with 2X Neopoints open with 24 hours on your clock and you open a second cookie that gives you 3X Neopoints, your clock will not be updated until the time runs out on your first cookie. Then, the countdown will be updated with the 24 hours that you get 3X Neopoints for.
This situation also works in reverse. If you have a 3X cookie open then open a 2X cookie, the 3X cookie must run out before you start receiving 2X Neopoints on game plays.