PWM output while using I2C with the ATTiny library
This is normal.

Timer0 is used as the clock source for the USI. It's the only internal clock source that can be used. The only other option is to use "software polled" mode where it's up to the sketch (or support library) to manually create the clock signal (less than desirable) by setting a bit in a register at the right time.

So you can only use Timer1 for your own (PWM) purposes while using the USI.