Hi,
UE will start on-duration times once UE went into DRX cycles. One DRX cycle means (on duration + off-duration ). when on duration timers runs then UE will be in on state. once it expires then UE will go to off mode till ( DRX-cylce - on duration timer). then again on-duration time starts and so on....
Inactivity timer means while in DRX state if UE receives data then UE will start inactivity timer to receive all the data, till inactivity timer expires UE wont got to off mode irrespective of anything..