That's essentially what I heard from my loved ones also stuck in (South) Lebanon about what "stay put" and not safe to evacuate right now...that it was more a "don't everyone rush to the embassy thinking we're putting you all on the two choppers and taking you all at once" type thing.
That apparently, from what they were hearing talking to the embassy from where they are holed up, that when word got out that American forces were on the ground to begin evacuations, that the embassy was being inundated and that THAT wasn't safe (people congregated, out in the open, nowhere to get for cover quickly, and night coming quickly, etc.) and all those people need to "stay put" until the advance team has everything set and THEN they are STILL planning to evacuate the Americans (that want to/can be reached/etc.)
I didn't know you had family stuck in Southern Lebanon, mfccinsd; please keep us posted and many, many prayers for their safety.