There's definitely power going to the Leviton timer. Here's the wiring diagram.
To reiterate, the white wire from the timer was connected to a bundle of wire with a yellow cap (assuming this bundle contains the neutral house wiring, light fixture, and fan motor). The single gray wires were connected to the black and red wires of the timer, which is now connected to terminals of the switch. The bare copper wire was connected to the green wire of the timer, which is now connected to the ground terminal of the switch. If this looks right to you guys, then I'll definitely look into checking the fan motor.
My electrician is definitely playing tricks on me when the house was built. I have no clue which breaker the wiring for this bathroom is connected to. I literally shut off power to the entire house.