In the game I just played, for me, this site showed
me and my opponent in the wrong player-tabs.
(the upper-right of the page, where it shows
player-names and number of captures and time-on-clock)
I still have that window open, in case keeping it open helps debugging.
The player-tabs display correctly when I open it in a different window,
either from my profile or by copying and pasting the url, and based on chat,
I believe they were also showing up correctly for my opponent.