we have two macs running maya, the other day we started a render on one but the results showed up on the other strange enough.
although odd we decided to carry on as the deadline cometh. later we kicked of a render on each but the results for both were alternately flicking in the result pane of only one mac.
the macs are on the network and we are sharing texture files from server etc but they are not set up to be slave or master and are not set for network rendering.
my guess is that you're both working from the same project folder on a network drive and thus both maya sessions on different computers are trying to access the same log, and the same images directory. This happens especially during interactive renders when both people render at the same time, one machine finishes first, when the second machine refreshes the finished rendered frame in the render view, it pulls up the other maya render because they both wrote to the same temporary image file. I've had this happen at a small house before.