You need to see information like this...
(Leviton DZPA1 shown)
If it doesn't include "Motor" or "Inductive" specifications, I would not suggest using it for a desktop fan. You can probably get away with it for a bathroom exhaust fan, they are quite small motors and the inductive kickback doesn't have large current behind it. It's all Luck based... how large are the contact pads in the Relay vs the current kickback.
I have a GE Fan Controller:
I just now opened the package
I bought it back when I was on the verge of giving up waiting for a canopy based Smart Fan controller. I was going to build these into Junction boxes and nail one box per fan up in the attic space. I'd hard wire them in was what I imagined. Then the Hampton Bay Fan controllers came out and I put this idea away. But this morning, I popped open the GE box and wired it to an old outlet.... I'll see if it works
There's no chance of me letting the Magic Smoke out, right?