"wednesday 20:04-21:04" (actually I believe you should join before 21:00, then fight starts) - is for Raid dominion. I.e. you need to form a small raid (doesn't need to be full) and join a fight that you signed up for (placed a bid) before the end of Monday the same week.
To place such bit you need a currency that your guild receives for group dominion fights on Sunday (only champion fights count I guess). To join champ domi fight on Sunday you need a group (not necessarily full) one member of which has champion tabard. You just sign for Champ domi in Ctrl+M window. Fights start at 20:00, 20:30, 21:00, 21:30.
I think for the fight itself you receive some amalgams and BG emblems. For the score/place your guild finishes with you receive realgar on Thursday.