First, I suspect that fans do NOT "turn off", but that is possible. What MAY be happening is that when they are running slowly they are so quiet you do not realize they are still running.
This MAY be what is going on - it applies to certain CPU chips (not all). SOME recent CPU chips have an odd quirk. When they go from idle to some increase in load their internal temperature sensor for a brief few seconds detects a very high temperature, then the temp settles back to perfectly normal. For that brief time the CPU_FAN header responds to that high temp reading by speeding up the fan, then slows down when the temp reading goes down again. The ACTUAL temperature spike is normal, brief, and harmless, so there is no reason to worry. I do NOT know whether this apples to YOUR system.