I think you answered your own question. It is presumptuous that she is linked to Empath 24/7. And thats why for that brief moment where he stuck his head out of the gate he didnt get the chance to warn her.
This is supported by her coversation with Empath. She didn't give him a list of exact instructions he acted on his own accord with her blessing and relayed information to her when he got the chance.
Beasts memo does suggest mistrust of Sinister as he is Sinister. But with the lack of proof theres no way to act which is why he suggested a telepathic interrogation of Sinister.
Nightcrawlers mind had a time lag. Its stated in the earlier issues of HoX that Cerebro IIRC does scans every few days . With the Crucible I'm guessing they know these mutants are gonna die and back them up right before.
I'm also looking at the issue with Synch. He didn't die instantly and managed to contact the Professor in time which is shown on panel. Cerebro didn't auto back up
While Empath was "hey what are you doing" then he was dead