Many / most modern power supplies control their own internal fan's speed, similar to what is done by a mobo for case cooling fans. This means the CPU fan may start up right away when first turned on. But a few seconds later it may slow or even stop, and stay that way until the PSU heats up under load. Then it will run slowly, and speed up as needed.
Corsair have recently added a semi-fanless mode to some of their others PSUs (besides the AX series). So yes it is normal for the fan on your TX650 to not spin, especially if 650W is overkill for your system.
One of the 'signatures' of the new TX series is that the fan spins when the system is first switched on, to demonstrate to users that the fan does work (in an attempt to stop people complaining that their PSU/PSU fan doesn't work) and then it stops.
I have a tx650 v2 and my fan always spins.
Like I said it is a recent addition to the TX series.
Quite thankful to hear that,I didn't know about that feature either as I just bought one and was going wtf? It spins at startup or when first turned on then stops. I've tested under quite a heavy load already and still haven't seen it spin up yet. Mind you the case was open and I kept feeling all areas of the psu,and was only slightly warm 70-75F at most and at one time maybe around low 80's F.