It works the same as Sync/Cute Charm/other "increases chance of encountering X" things, except only if you haven't seen all Unown letters.
RNG call > if X encounter new Unown shape / if not X proceed as normal.
On amab's map the result was not X, but the letters changed because the RNG call happens between IVs/PID and Unown shape determination.
I must admit I can't say I entirely understand what you meant there, Dark Ray.
However, I tried activating one puzzle (Kabuto), then catching all the Unowns I had already caught earlier (I'm just plucking them from Pokegen, not to waste balls; therefor, every catch was a fresh catch). From the Kabuto puzzle, I was missing B, E, G and I. I got the same ol' F from the regular try, but when I did the Mysterious Transmission, I found a G! And after catching that one and hitting my seed again, I found an I instead! So, I might actually be able to finish up all the Unowns this way.
Both catches were done with different Seeds, but I'm guessing that doesn't matter.
Edit: did it the third time and got B now! :D
Edit2: and finally, I got E too. Great, this works lol!
Edit3: I sadly cannot get the ! even after having caught all other 27. Makes me sad. I will have to RNG a whole new file and unlock all of them just to complete the set. X( (and pray it even triggers the darn thing too. Well, I know that a certain HP Ice spread triggers it so I could go for that I guess...)