I think the class name `timer-ring` is less clear when taken on its own. It's not as obvious what about `timer-ring` is variable--might the other classes be `timer-{action}`? Or `{source}-ring`? To me, `from-timer` is a little more obvious (although `to-timer` is another possible variation, it doesn't really make sense in this context). This is also why the `data-*` attribute is best: only the variable part is in the attribute name.

Really, though, what's important is the code structure. If the names make sense together, that's enough for me. I may have been in a weird mood 20 days ago because `timer-ring` is now only minorly unsatisfying, and I'd be okay with either choice. Or maybe I'm in a weird mood now.