I would have to say that the second Mythos card does NOT meet the Rift criterion of "Each time a mythos card is resolved," since the card is NOT being resolved, but largely ignored. If the rule for Rifts where "Every time Monsters moved," that would be different.Except that "every time Monsters move" would require that Monsters actually move. The Rift mechanism merely requires you to check whether "the monster movement pattern on it matches any of the patterns next to a closed rift". It's the symbols that trigger the rift, not the movement of Monsters.
But (and I have a big but) it's the "Resolve a Mythos" aspect of the Rift mechanism that is important (as you indicate) and the Rumour certainly isn't asking you to resolve a Mythos. So I agree with your evaluation Radulla (should that be worth anything at all )
What would make the Rumour totally nasty would be if the Rift mechanism said "every time a Mythos is Drawn, if the monster movement pattern on it matches any of the patterns next to a closed rift...". Still, that would be the more fun way to interpret it; anything else would be the decision of a lightweight