I would provide a link, but it's just an excerpt that may not be accurate."But we didn't know—" She broke off. Her light eyes went quickly to her husband's face.
"It is from him she takes the Greenwich time," said Poirot to himself.
Like other contributors, I have never heard this metaphor before; and all the (few) references I found on line pointed back to Agatha Christie's writing.She takes the Greenwich time from him.
Is it some kind of metaphor or proverb?
I certainly don't understand it as "punctual", but rather as "she does everything as he tells her", he controls her, or rather, she let herself be controlled…No, I've never come across this before either. I agree with MM that it's not very intuitive. I would have taken it to be a variant of She sets her clock by him ~ i.e. he is extremely punctual.
Yes, she takes his words as gospel.I'd rather take it to be a variant of "She'd believe black was white if he said so".