When a hidden or contained problem (the shit) is suddenly exposed or spirals into utter chaos (shit making contact with rotating fan blades) causing a change of tactic from problem elimination (disposal of shit) to damage control or abandonment (cleaning of all traces of bits of scattered of shit or escaping as situation is now unmanageable)
The point at which "the shit hits the fan" is the point at which an already unstable situation devolves into utter chaos, often in spite of--or even due to--a higher authority's attempt to control it.