It does, but I think the water is heating up between the tap/mixer, and the spout. If it was inbetween the valves, the last valve would be having more issues.

Consider this: the water between the tap/mixer and the open end of the spout is like a glass of water, so full the water's higher than the surface of of the glass (held there by surface tension.) If you were to heat that glass, the water would start to overflow.

Provided it doesn't leak normally, I don't think you should worry, and I doubt there's much you can do about it, unless you turn off the shutoff, and open the tap to allow it to drain a bit, then turn it off.

The only time it might be an issue would be when you're melting chocolate or something, where water would cause an issue.

A different tap or spout that could swing more out of the way?

Did you install enough CFM for your vent, and are you using it? It's not just for smoke and grease. It removes excess heat as well.

I've got 1200 CFM and yes I turn it on but it doesn't matter. The leaking only happens with the dual griddle (24") is on and it only starts to leak after the griddle is nice an hot. I will try to empty the pot filler first and see what happens. I'm just worried about long-term damage to the valves as a result. Should I be concerned?