2K2? You need to use something adjustable to set the centre stop. e.g. the maplins pot.

The servo doesnt move when first turned on with the Tx off because there are no pulses received.

When you turn the transmitter on, the centre off isnt correct with the fixed resistance so the servo turns slowly. You could trim this out on the Tx.

Then when you turn the transmitter off again, the failsafes kick in, but are outputting the wrong setting to stop your servo. If you take the failsafes off, you will see the servo stops when the Tx is off.