So I've downloaded the manual for the KORG Module app-- and even bought it since it's currently 50% off-- and had a look at it. I've also had a look at the manual for the MX49/61/88.
If you're able to select patches using other keyboards then I assume you already know about creating a Set List in the KORG Module app. As I understand it, this will determine the Program Change values which will select each of the patches that you want to play.
The MX61 doesn't have a "Send Program Change" function per se; it simply transmits the Bank Select, Program Change, and other MIDI messages whenever you select a Voice to play. I don't think the KORG Module app cares about the Bank Select-- hopefully it will just ignore those messages-- so the only "trick" will be choosing a Voice that uses the particular Program Change value that you want to send to the KORG Module app.
I can think of three methods you could try to use for sending Program Change messages from the MX61 to the KORG Module app:
(1) You could just select a Voice that has the desired Program Change value. That could be a hassle, because the preset Voices aren't organized in order by their Program Change values, so you'd have to look up which Voice to pick on the MX61 to get a particular patch; you wouldn't be able to just scroll from one Voice to the next to select the next patch in your Set List.
(2) You could create your own list of User Voices (or whatever they're called on the MX61), such that User Voice 1 will select a Voice that sends Program Change 1, User Voice 2 will send Program Change 2, etc. You could even have each User Voice send specific Control Change messages to modify the selected patches. One drawback of this method is that it would keep you from being able to use your User Voices for the MX61-- assuming you want to use the MX61's own Voices for some songs.
(3) You could create a set of SMFs (Standard MIDI Files) that don't contain any Note On/Off events, just Program Change and Control Change events. For greatest convenience you'd probably want to name them sequentially, such as calling them SONG001.MID, SONG002.MID, etc., up to SONG100.MID, so you can easily scroll through them and select them in order by their names. SONG001.MID would contain a Program Change 1 event, followed by any Control Change messages you want to use for setting up Patch 1 of your Set List. Likewise, SONG002.MID would contain a Program Change 2 event, followed by any Control Change messages for Patch 2; etc. The benefit of this method is that you would still have your User Voices, or Performances, available for the MX61's own use, plus you'd be able to store the SMFs on a USB thumb drive so you could have different sets of SMFs for different song set lists.
I don't have any of the MX models, and have only just bought the KORG Module app, so I haven't had a chance to try using any of these three methods with my PSR-E models yet, but I think they should work.