Dominion spread doesn't seem to conform to what is announced in the manual
See
the discussion in this thread for details, but independent testing made by various people strongly indicates that dominion spread does not follow the "rules" as described in the manual. Namely, the chance for successful temple checks don't seem to really increase with number of temples.
One possible hypothesis, which seems coherent with experimental results, would be that the chance of successful "check" from the home province (and maybe prophet or pretender) does increase with number of temples, but checks from temples don't.