This doesn’t seem like two actual dimensions of time. It’s more like Special Relativity, where the timing and ordering of events depends on the observer’s frame of reference. So for a given event two observers would apply two distinct timestamps. That seems to be what’s going on here. There’s only one time dimension but observers perceive it differently.
(The similarities between distributed systems and Special Relativity are pretty well known. I’m not sure who first pointed them out; probably Butler Lampson.)