Did you have the top strip done or the whole windshield?
If everything was working when you took it in for tinting then that is most likely the issue.
I'm not sure what year yours is but there is a warning out for the 5th gens based on all the electronics under the dash.
A lot of shops in my area won't touch the windshield (other than the strip on top) for that very reason.
It might dry out and work but it also might be damaged. I don't know how long ago you got the windshield done but I would go there and show them what's going on and that it wasn't like this until they tinted the window and see what they'll do.
Some installers are more cautious about where all the liquid goes than others. Did you sign anything that would release them from liability for any damages based on your request?
Very few states allow for the whole windshield to be tinted so there might be a liability clause for the shop saying that anything outside of allowed state regulations are the responsibility of the customer (fines, tickets, and damage from performing the illegal request).