The Timeys are a secret society that has been around for centuries. The Time Keeper joined when the Time Master posted a flyer for a meeeting in the window of Longo Watch Repair.
The Time Master revealed the story of the beginning of Time. Todd Rysdale, a muscly shirtless human male, said, "Time shall be!" And thus was Time created. A terrible alien monster with an octopus head named Dorthax wanted to stop Time, but Todd threw a net on him.
During their Leap Year Celebration in Episode 404, the Timeys turn out to be a sort of Scientology cult. They are trying to wring money from the Time Keeper, and when they make him say, "Time is money," he refuses and throws them out, cursing time. He vows to wander the earth, hating time.