You're right, I think. I believe that once you bid on a guy (and he ends up on your bids page) the time shows up as your local time. Before that, if you click on his page, it'll show his end time based on the local time of the clock in the top right corner. Let me repeat...I think!
It's certainly confusing, and though I like seeing what time people will end in local time, it can get pretty confusing. For instance, there have been times when I've seen a guy who I thought was almost ending and panicked to bid quickly, then when the time transfers hes actually not done for another 6 hours, etc.