Getting two servos and RGB LED working together

I am not sure I understand how PWM uses timers

PWM turns pins on and off very quickly, to simulate a variable voltage output. That toggling happens when a timer interrupt happens, and the PWM-set interrupt handler says it's time.

and there is not enough timers to go around.

Compromises need to be made. An unlimited number of timers (one per pin) just isn't practical.