Back speaker grill(?) got wet during tinting. Should I be worried?

Wow. Most shops cover the area with a few towels and try to dab the corners just for professionalism but no this isn't going to damage your speakers or cover. You might see a residue if it wasn't wiped at the shop. I use Adams leather and interior cleaner on a microfiber towel on these areas, front and back and on the headliner for the make up finger marks.
In the old days, water would F- up a speaker. Unless they filled up with water, it should be no biggie.

 

There's no speaker under that grille. I wouldn't worry about anything other than possibly some residue to clean up.

 

I couldn't agree more! BTW- Magic and James (Big Game)... Two of my favorite Lakers!

 

Be sure to check the middle brake light housing from outside the car. If they got that much liquid in that area you may have some streaks on the inside of the glass.