I stopped using stuff like this many years ago.
There are many reasons.
1) Most new gear simply isn't made to be cleaned and lubed with this stuff... especially the cheap "sealed" pots. It seems like you were lucky or smart enough to have selected a product that doesn't actually melt and ruin the parts... which is something that can easily happen with the newer plastic housed parts. I've done that... and once was enough. :-)
2) Many times introducing lube to older units, the ones that are designed to be serviced, simply initiates a scenario where the lube attracts even more dirt and grime than was there originally... and then the noise slowly gets worse than it was before cleaning. The situation is like a cat chaing it's tail.
3) I have found that vigorously moving the fader or pot for an extended period of time is the most effective way to reduce and minimize the instances where movement causes noise.
Having said that, and I regret having such a contrary attitude for the situation you find your self in, I'd say that the "wetness" you are observing is simply the oily slime mess left by the mineral spirits listed as the vehicle in that clean and lube product. I suspect, but can't guaranty, that you can power up safely after just a few minutes just as the instruction claim.
The oily slime left by the mineral spirits will attract dirt and dust and eventually, if not sooner, you can consider cleaning it, or not, again.
best regards,
mike