Don't confuse tides with current. Tides only effect the current going into or out of the barries reef of Palau. The currents along the popular dive sites are a function of surface winds and major ocean currents. This tides only effect three common dives sites in Palau (Malakal Channel, Oolong Channel, and German Channel).
Malakal and German channel need to be done on moderate incoming tides (any time of the month). Oolong is best when done on a ripping incoming full (or new) moon tide to get the superman effect. Some people also prefer to do Chandelier cave on low (full or new) tide to be able to get to the last air passage in the back.
Depending on when high tide is during the day, your boat driver may have more options of how to get you to the dive site (owing to the number of patch reefs inside the lagoon), but you will always be able to dive your dive site regardless of the time of month.
I would be more concerned with time of year than time of the month. If you want a ripping Oolong channel dive, make sure you plan for a full or new moon, and make sure the operator knows that you took the extra time to plan it that way so they take you out there.
My 2 cents.