Doesn't what's written in point 3 of the rules bother you? :D
Everything is described according to the games.

Doesn't it bother you that it's not described how players determine a random template and pair? Does the judge do this for them? Or do they do it themselves by generating the first map in IRMG and then generating what resulted from the first one (while it's unclear what the template was in the first random generation)?

It's obvious that playing the first game with one restart, using 3 different random pairs and templates, or playing 3 restarts with a pre-determined pair and template are fundamentally different things.