Just to state the obvious, the meter gives you a reading, and a positive offset to that reading.
If it says 1/125 at f/16, +5/10, that means 1/125 at f/16, "plus half a stop". How you compute this half stop, as aperture or shutter time, it is totally irrelevant.
Normally though if you have an old-school lens you would certainly see this, in your mind, as an aperture modifier, because normally you can place aperture anywhere (they don't have to coincide with "clicks", you can close the diaphragm "1/3") whereas with shutter times you are not guaranteed how the shutter time works in intermediate positions between "clicks". Some shutters might even be damaged, maybe. Diaphragms, on the other hand, are 99% of the times designed to be closed "continuously"(*)
So if the light meter tells you 1/125, f/11 plus 2/10, and you want to use exactly that value, you can set the aperture ring just a little bit past f/11.
I agree the main use of 1/10th of stop is to check luminance rations, and even illumination of background, etc. in studio work. Otherwise makers would rather make lightmeters work in 1/3, or 1/2 of a stop.
Fabrizio
(*) This might not apply to your lens. Your mileage may vary. Do any experiment to your own risk. By reading this text, you acknowledge that no damage, present of future, will be claimed from its author. Etc. etc. etc.