I don't know the mechanics, my guess is they translate the MIDI notes to the scale given to them by a tuning file

Here's a pretty comprehensive-looking list of software instruments supporting microtuning:

https://en.xen.wiki/w/List_of_microtonal_software_plugins

I don't know what all the options are, but MTS-ESP is one. If I understand it right, it's a sort of out-of-band channel where you can apply tuning tables to all the MIDI synths that use the MTS-ESP API from one place.

I think it's not sent over MIDI so it only works if everything is running on the same computer.

https://oddsound.com/mtsespsuite.php