Time will only be added to your countdown clock on the Wild Card Fortune Cookie banner for a cookie has the same Neopoint multiplier that you currently have.
For example, if you currently have a cookie with double Neopoints open with 24 hours on your clock and you open a second cookie that gives you triple 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 at triple Neopoints.
This situation also works in reverse. If you have a triple cookie open then open a double cookie, the triple cookie must run out before you start receiving double Neopoints on game plays.