the fan should never completely disengage, it will always spin, but most of the time it will be spinning MUCH slower than the engine, so very little drag on the engine, when the engine gets too hot it should NEVER disengage based on RPMS, it should stay engaged until the temperature gets back down to where it belongs (180-200 *F).

on a cold start the fan is often engaged and will disengage whenever the fluid gets distributed properly by centripetal force. There is no set engine speed where this happens, mine usually lets go about the time the trans shifts into 2nd gear, and always by the time i hit third. however you can make this happen sooner by gunning it real quick when you first start off, or before that in park and it should help redistribute the fluid and disengage the fan

i hope i answered your question if not feel free to ask again