Took me a long time to figure this out, even though it seems simple in retrospect.
In many finger twirls you're rolling along the back of a finger. This is easiest with a simple stick or baton, because both ends are weighted the same. It's harder if one end has more mass than the other. And it's harder yet with a "tourist" type of cane, with that J-shaped handle, because the mass is concentrated one one side of one end.
The secret is to watch the hook end at the safest part of the twirl, where the cane is within the fingers rather than atop the fingers. If the crook of the cane points up at this part of the cycle, then it will naturally point straight down 180 degrees later, balanced -- it won't roll around on the back of your hand trying to rebalance itself.
For a smooth roll over the back of the fingers, try making sure the hook is pointing straight up when it's within the fingers, because you'll want the weight pulling straight downwards at the tricky time.