Sound from timing belt or water pump?

I just recently got my timing belt and serpentine belts replaced (2weeks ago) and immediately upon receiving the car back, a sound started to appear that had never been there before. As soon as I turn on the ignition, a low-pitched rotating noise appears, as if there is friction from something turning. As I start driving slowly, the noise gets more frequent as the sound intervals of the rubbing are becoming shorter because of the faster rotations of something (my knowledge about cars is minimal idk what this "something" could be). I brought the car back to the mechanic today, drove around the parking lot with him so he could hear the sound. At first, he said it sounded like it was coming from the breaks, which I thought was ridiculous. I left the vehicle with them, and the mechanic who had been in charge of replacing my timing belt the previous visit called me bak with a diagnosis: apparently since the new timing belt is tighter, it causes stress on all of the pullies and bearing etc which causes the water pump needing to be replaced. He quoted me $575 to do this.

To me, this sounds like I'm being ripped off and given a weird and unnecessary diagnosis. Since they were in charge of the timing belt repair, shouldn't they have driven the car and tested it instead of just handing it back to me with a noise? Apart from the water pump, they had also previously said that I need to get my head gaskets changed and my engine washed out/inspected and told me that I needed to change my cabin air filter because it was "REALLY dirty".... I do research to later find out that my model of tacoma doesn't even have a cabin air filter.... Anyway, some help and advice regarding the timing belt sound and its relation with the water pump would be great. Thank you!!!

PS I have ~100k miles on it

 

Why would anyone bother to change a timing belt and not change the water pump while they were in there? It sounds like the timing belt is rubbing on something, so maybe they screwed it up installing it. The new belt should be about the same tension as the old one because of the hydraulic tensioner.

 

Let me guess, you went to Jiffy Lube?

 

Probably one of your idler pulleys has a bad bearing.