Massive Spoiler Warning: The question discusses events very near the end of Neal Stephenson's Anathem.
When Cell 317 was up in space floating with the Cold Black Mirror, several members discussed having dreams that didn't feel like dreams, ie. were vey hard to distinguish from reality. During a conversation someone (I think it was Arsibalt or Jesry) mentions he's not sure if this is not a dream. Sammann even expresses surprise in that he "wakes up" to find the transmitter still working, although he clearly "remembered" destroying it.
This, along with the Millenarian's general indiference, leads me to believe that he had in fact started his Incantations from the very beginning of the launch - possibly even from the beginning of the Convox, and that the dream-states were the alternative Narratives the Millenarian was taking them through. We can only guess at what the Incanters were up to when secluded in their math, but during the Convox we have the following clues:
Fraa Jad is up all night at the Bazian monastery, chanting. This may be a way to just pass the time, it could also be that Erasmas was witnessing an Incantation.
When Jad spoke of the "Hooded Ones", referring to the hijacked Matarrhite peregrin, he gave us the hint that they weren't actually Matarrhites. This he could have inferred by observing flaws in their behaviour, like the ones Arsibalt pointed out when he confronted Vernes, or he simply visited some Narrative where their identity had been made known. The Steelyard makes me root for the former, but I can't completly dismiss the latter either.
The Teglon and the keypad. Again the Steelyard tells us that a Millenarian might have solved the puzzle (although many Millenarians had failed), or he could have made himself into a distributed syndev, brute-forcing the problem through many Narratives. But would he start an Incantation just for fun? Well he's an eccentric old Grandfraa, he might as well act like one.
During the Keypad narrative Fraa Jad tells Erasmas that
I am in several [Narratives], a state of affairs that is not easy to sustain
which leads me to believe he wasn't solving the Teglon just for the fun of it; he was practising.
In any case there must be clues that I've missed and I don't have the energy to go back to the massive book now that I've finished it. So my question is, as the title states, when did Fraa Jad start his Incantations, and how did he affect his Peregrin?