Just to clarify, this is what most brands approve for cleaning dials, meaning removal of loose debris from dials:
These cleaning sticks have a small blob of what I think is urethane at the tip, and clean dials very gently without leaving any residue behind. The blue pad is also sticky and is used to clean the tips of the sticks. This system works very well and I use it daily.
The basic Rodico (the green one), Rodico "Premium" (which is grey), or A*F's product called Rub-Off (which is blue) and any similar products are all forbidden by Omega and other companies for use on movements, dials, or hands as they leave a residue behind. I've said this before, but one of the first things the instructor at Omega did when I was their for training was tell anyone in the class who had this type of product in their tools to leave it there, because they don't allow it's use, and if you were caught using it you would fail the course.
Just to show some not so good outcomes with watchmakers cleaning dials, these were sent to me by very upset watch owners to ask my advice on what to do, and why a watchmaker would even think of cleaning the dials they sent them. This one was washed...removed some lume and generally made a mess of it:
This one was fully printed when sent away, but the watchmaker dipped the dial in "solvent H" to remove dust from the dial, something he says he does on every dial and is standard practice (it isn't). The result was loss of most of the dial printing, and to make matters worse, he didn't even mention it before sending the watch back, so the owner got quite a shock when he opened the parcel:
So in the case of the OP's watch, yes it turned out okay. I suspect the lacquer was removed, and if none was applied to replace it it's unclear how long the dial will stay nice, but overall it turned out about as good as these things do. But the risks of doing this can't be overstated, and IMO should always be done in consultation with the watch owner.
Cheers, Al