That thumbrest is a hit and miss thing. I leave mine off of my whistles in most situations, but when I have to whistle/sing/whistle/sing/whistle in quick order in the same song, I’ll sometimes throw a t-rest on it so that I can quickly find my mark without looking down. I prefer it in a spot similar to the rest on a sax…just near the third hole up from the bottom (the F3 hole on a D whistle) and with the thumb tucked just underneath. Can’t get the thing off quick enough afterwards, though, as I prefer to do without.
Just hold the whistle naturally, and position the thumb rest right above where your right thumb sits. As with Jef, I don’t find them much use for high whistles, but for a low-C or -D, they can come in handy.