As an engineer on ZS-Registered turbine types, the company used to book either collective up/down (206/105 etc) or wheels off/on for the rest. The Hobbs switch was either on the collective jackshaft or the squat switch.
Those were used to calculate maintenance intervals and what the pilots booked for revenue/logbooks etc was a separate, unrelated value.
Obviously these methods will differ from type to type and company to company as to how times are recorded, but most rotorcraft will be counted on flying time for maintenance.