Nice macro of the H558 movement you took with sub-photo of the rate trimmer.
If your Arnie is running a tad fast after you had the gear train cleaned and lubed, that is not out of the ordinary at all. I have experienced this gain of time to after a service, and my rate trimmer was not touched when serviced, so it makes sense that the cleaning & lube removed years of coating and some dry lub that is resistence.
I would not touch the rate trimmer just yet, as once these trimmers are adjusted, there's no going back after the adjustment. These are for usually a few adjustments throughout its life span from what I've read and been told.
Give the watch some time to smooth out again and adjust, to the fresh service with its clean freshly lubed movement, and it just may step back into the timing on its own.
(You can always adjust the rate trimmer after awhile)
If your a couple seconds gain, then you would turn the screw to the right side in your pic, ( by 1 click & 1 click only) as seen by the adjustment hash mark indicators, and then give it a good few days and recheck the timing.
(Then if still fast, then give her 1 more click to the right or counterclockwise, and check the timing after a few days, and that should be all you need)
Here's a time and setting guide for you as well:
I agree Catalin as well with what he mentioned, the adjustment you will make is turning the screw counter-clockwise or to the right as shown in your photo. But don't go any further than 1 click at a time only, then recheck the timing!
Cheers & good luck,