Mesaana knows foretelling always come true, but her (low) opinion of the talent comes from her belief that they usually become understandable only when it's too late for them to be useful, and them they're all too clear. It's Lanfear who dismissed prophecies as wishful thinking.

Alviarin did not embellish at all (she knows better than to do anything like that - she is trained to report verbatim and her POV states that she does). She reported exactly what Elaida said, including her claims that Alviarin could not differentiate from the foretelling (like the rebels breaking). That's the bit that attracted Mesaana's immediate attention (it touched on her plans) and she asked Alviarin right away if it had been part of the foretelling or not. Then Alviarin (who didn't have the answer - she couldn't tell) was saved as Mesaana mused it wasn't important to know if it was part of the foretelling or not, that either outcome she could use.

So Mesaana was aware from the start that the bit about the breaking of the rebellion wasn't necessarily part of the foretelling. It's more a matter of whether she (or Alviarin) remembers or not the rest about the purge and reunification and the BT which was part of the foretelling, but both Alviarin and Mesaana seem to have an excellent memory.

I wouldn't bet too early that Mesaana or Alviarin didn't remember the foretelling and that it didn't factor into either's late TGS plans.. That could be the explanation how the BA/Mesaana understood lightning fast what was about to happen and decided to escape from the WT, that either figured out they had hours at mos, before the whole game was up. Elaida's foretelling would reveal the only way out left for the BA was flight... Elaida gone and Egwene saved there was only one Amyrlin left, and the foretelling said she'd win and make the Tower whole and stronger than ever, and the BT would be rent in flames...

Consider that this occured hours after the Tower leadership collapsed (Elaida captured, and previously the Keeper and Red Sitters vanished), the Hall no doubt in an emergency meeting, and Egwene had escaped after turning the Seanchan back, opening the door open for a precipitated reunification (if you are willing to see things as they stand for real instead of delusion yourself, Elaida-style.. Either Mesaana or Alviarin was very lucid about how things really stood at that point), and only a shortwhile after envoys were sent to the BT. With their knowledge of Elaida's foretelling,

Mesaana (or Alviarin) could puzzle out, especially if they were warned something was happening at the rebel camp that night, that their games were over and "the tower whole" was about to happen, and.... that a remnant forcibly would escape... to be cast out and scorned... Elaida's foretelling might have factored in the decision to send the rest of the BA out immediately, especially if we discover in TOM Mesaana didn't show up when a panicked Alviarin called her (Mesaana might have concerned herself that night with how she'd manage to remain hidden in the Tower), and Alviarin made the final decision herself to order the flight and warn SH. It seems many BA were caught, because even with an emergency measure of some kind to communicate (that'd be something like Alviarin Travelling to the bedroom of each SC members to order them to go wake their heart and fourth, and order them to pass the order down in person then flee), the BA system was still not up to the task of achieving this in hours, not with so many broken hearts in the chaos after the Seanchan attack. Some BA might also well have panicked and fled before passing the message.

That a rebel BA who escaped gave the alarm in the WT is not so likely (they couldn't know this wasn't also happening in the WT, for one thing), at least unless one of them had a way to reach Alviarin or Mesaana directly, which is unlikely as both are security freaks. As for non BA spies (DF), though it's extremely likely there are some among the rebels, it's hard to see how they could have learned what Egwene planned (the assault, I mean), as Egwene played this very close to the vest and acted damn fast. it's not obvious a non AS spy could reach Mesaana that fast in the wee hours... There remains the possibility Mesaana herself came to spy (visit Sheriam, for eg - and found her not) the second she learned Egwene was gone, to find out if Egwene had gone to the camp, if she knew Elaida had been captured, and what she planned next, and Mesaana realized what was going on. But would Mesaana have cared much to save Alviarin's cohorts, though? Make it a priority? In fear of SH's wrath, maybe...

It's a pity that storyline didn't run in parallel to Egwene's. It would have made it all more suspenseful/exciting in "real time". Now the real mystery left is where the BA has gone. How the BA managed to escape remains quite interesting, but we'll know the final outcome all along.