This all depends on the orders. If it's Title 10 then it is Federal active duty under federal control. If it's Title 32, then they are still considered under state control, and there is also another type of activation called State Active Duty when they are called to active duty by their governor in support of their state only within their state, which only counts as working for the state, not any type of real active duty military service.
Source: Former Army Reservist and National Guardsman. Me.