Hola William 

This is a tricky one because, as you are saying, you'd think the agreeing adjective would be in feminine, matching with "la gente" or "las personas". However, when we use it in masculine what we mean is:

... muchas personas se reúnen en este lugar frente al reloj para comer las uvas [TODOS] juntos ...

Even if we used "mucha gente", (feminine singular), instead of the plural "muchas personas", we would still say:

... mucha gente se reúne en este lugar frente al reloj para comer las uvas [TODOS] juntos ...

It is as if "juntos" here took a different role in the sentence meaning "gathered all together" detaching from the subject (gente or personas).

I hope this clarified it.

Un saludo

Inma