That's the exact remote humidistat I bought thinking it should be able to work, as you say, even when the light is off.
I queried it with the electrician - he says that the fan will always work with the light regardless, then run on, until humidity is gone.
I don't know, maybe my expectations were back to front about how they actually work - I thought they woul detect moisture THEN come on, rather than having to be turned on then use the stat to turn itself off. If that's the case then this remote stat is doubly redundant - no point in having the sensor if you have to turn it on manually anyway, and then no point in having the run-on timer if it's going to use the sensor to decide when to turn off.