I have been sent the following answers to the above question:
1. From Dr Spencer N. Axani, of the CosmicWatch project:
Thanks for the email. It [the muon detector software when two detectors used in coincidence mode with one physically placed on top of the other] cannot distinguish who [which of the master or slave detectors] is on top. The timing resolution is order 30us, so you would have to have them separated by 10km [in order to be able to distinguish them in that way]. The muons are highly collinear with the incoming cosmic ray, and point back to the cosmic ray interaction in the upper atmosphere. The angular distribution of the muons can also help determine the muon lifetime; it should follow roughly a cosine squared shape.
Dr. Spencer N. Axani
2. From another observer on the [muon-detector] IO group:
Another observer on the [muon-detector] IO group pointed out that muons do not come from the earth below the detectors but from the atmosphere so I do not need to worry about the detectors picking up terrestrial muons from below.