Tournaments are playable in IE, yes
The sorting in each line depends on the UserID, this means your 2nd round with 4 players left is sorted by UserID from left to right. That's why "jessicajoanne" moved leftmost, seems this user has the lowest UserID.
This User also should move up to the Final, that's right... Hmmmm, I will check this again.
Please test 2- and 4-player-Tournaments, they should work well ?