In the frame of reference of the ants, all clocks agree with one another. This means that timing is global within their FOR. There is no problem in determining simultaneity because there is only one FOR in question. And even in multiple FORs, their relative speed would have to approach that of light for any ant to notice a difference between local times. Deny at your own detriment.
I don't think you really read the article since the author never said that parallelism is inefficient. He's saying, among other things, that decomposition (which you seem to favor) is not the right way to design parallel programs. In other words, if sequential objects are used to create sequential programs, it follows that parallel objects should be used to compose parallel programs. Sequential order thus becomes a consequence of signaling, i.e., communication between parallel objects.