Just out of curiosity, does a tech priest need t5o keep a copy of the uplifting primer or does being assiciated with the AM mean he doesn;thave to, or can claim he has a copy in his memory banks?

He isn't an Imperial Guardsman, so I'd say they neither expect him to, nor expect him to live up to the ideals a "real soldier" would; they believe weird crap, about weird machines, anyway. It's less likely their machine will flip out, then the Psyker's head will rupture, and Cthulhu will enter our world, looking for victims, but I expect most Specialists get some of the same weird looks. Of course, nothing says the TP WON'T have a copy, if only to try and figure out what makes his Guard allies tick, and work better as a unit, but he probably hopes to get promoted to real AdMech responsibilities, someday, where those details won't matter.

While Tech-Priest Enginseer is a member of Imperial Guard formally, in the first place he is a member of Adeptus Mechanicus, who just decided (or was sent) to work in this field. Theoretically some Colonel or Comissar can try to demand him to carry Primer and Munitorum Manual... but this is not very wise course of action. On the other hand, I think, any Enginseer would download all regulatory documents of IG into his Cranial Circuitry just because they are regulatory documents.