At Envoy, yes, you must fatigue to avoid extension which involves filing a fatigue report. Depending on what is said in the report, you may or may not get paid. I have not had to fatigue but apparently they are looking for documentation on details to prove why you are fatigued (noisy hotel... what time did you call to complain at the front desk/did you file a complaint with the company for the noise, etc).
ALSO, I have heard that depending on what is in your fatigue report and what you say on the recorded line when you call in fatigue, your fatigue call may be turned into a sick call or even a missed assignment. Again, not from personal experience. I hope those are just crew room stories with a "there's more to the story" caveat, but I don't know.