I would like to know how to understand the construct “Jetzt heißt es” and then use it in my own sentences.
De.wiktionary.org explains one meaning of the verb heißen as “es heißt: es gilt” with the example:
(1) “Jetzt heißt es aufpassen!“.
I have also found another example online:
(2) „Nun, jetzt heißt es "alle Mann an Deck", Miguel.“
The closest I can come to a meaning is „Now it is time for“, which fits example (2) but not really (1).
Taking the literal approach (note that "jetzt heißt es" is an inversion of "es heißt jetzt", sounding a bit more poetically):
So far, so good. But what does "es" refer to? It's the activity to be done by the addressee(s)!
To piece it together: "Now, the activity we/you should do is (called) X", or more colloquially: "Now, we/you should do X".
Note that whether "we" or "you" is used depends on whether the speaker includes himself in said activity (a teacher saying "Jetzt heißt es aufpassen!" will likely not include himself, whereas a colleague saying "Jetzt heißt es Mittag essen!" probably wants to eat lunch, too).
In general, this idiom is used to convey an action that has to be done without using imperative directly (which can be considered impolite in many circumstances) or to convey an action that is inevitable ("Jetzt heißt es Abschied nehmen." - "Now we have to say farewell."). It's also a passive call to action, omitting the original caller so the speaker is able to distance himself from the order - even if he is the one who calls it (maybe he doesn't like it, or he has to do it because of rules so it's not his decision).
To look at your example phrases:
Jetzt heißt es aufpassen!
Now you'll have to pay (close) attention (, because what I'll tell you next is important)!
Nun, jetzt heißt es "alle Mann an Deck", Miguel.
Well, now we have to go on deck, Miguel.
or, more colloquial/keeping in line with the original
Well, now the order is "all hands on deck", Miguel.
EDIT: Of course, there's always the literal use: "Jetzt heißt es 'Bundesagentur für Arbeit' (statt Arbeitsamt)" - "Now it's called 'Bundesagentur für Arbeit' (instead of 'Arbeitsamt')" (= the German Federal Employment Agency)
Nothing is special in the phrase, except usage frequency. It is just employing meaning 7 listed in Duden, that something is necessary to be done. Since it is correctly marked as formal language level, don't expect it in conversation in other combinations than *Jetzt heißt es, *.
https://www.dict.cc/?s=jetzt+hei%C3%9Ft+es
I think this answers your question, with a special entry dedicated for the first example.
"Jetzt heißt es aufpassen." is translated to "Now it's important/vital to pay attention."
