Umm, you've sort of got it.
You don't actually ARM the A/THR as such. The arming occurs by default when you put the levers in the FLX, or TOGA detent.
It is activated (again by default) when you place the levers in the CLB detent at thrust reduction alt.
To disarm it, you can do any of the following;
press the button on the levers.
set the levers to idle.
push the FCU button (non standard)
stick the levers anywhere foward of the CLB detent
(The above all applies to all engines case. Things change a little when eng-inop.)
Diconnecting it is a matter of personal preference, and also dictated by A/C type. In gusty winds, most I work with disconnect it, and fly manual thrust from 1000' down. The A330 A/THR (with RR engines) performs quite poorly compared to the A340 in similar conditions.
The A/THR is a function of the FMGS, much like the FD's or autopilot.