The tip protector is designed to be placed over the bottom tip. It's only purpose is to protect the tip if it is placed on the ground. Keep the finish from being rubbed off, which in turn will keep out the dreded moisture.
I don't care for leather because unlike rubber or plastic, it will allow moisture in, it gets wet from dew, rain, and humidity. I prefer rubber, then plastic. I recommend taking the rubber or plastic off if you are in the rain for extended periods of time, or if you happen to to take a tumble in the drink. Take a clean dry towel, remove the string, wipe and dry off the bow tip, and allow to air dry. I then take a Q-tip, dipped in alcohol, rub the inside of the tip protector. The alcohol will cause the water to evaporate faster. Take the other end of the Q-tip and swab the inside of tip dry. Rubber tip protectors can easily be turned inside out. Let it set for a while, in a place where it can air out, and then return the protector to the bow tip.