I don't know a lot about JS, and I know nothing about Voat's code base. I assume clicking/tapping the up or down arrows triggers a function which reports to Voat's server an event and locally modifies the style so it appears clicked. That seems to me like it would be pretty straightforward, if that's the implementation.

I've noticed it can take several seconds for my votes to register. It is evident that the vote has not been reported to the server when I click an arrow then click on that subverse's name shortly after. I'll see a new page with that subverse's content including the submission I wanted to vote on, and the number hasn't changed nor has the style of the arrow, indicating to me that my vote never made it to Voat.