You're rusty. 
The four triggers I posted are not restricted to Byzantine characters and therefor cause non-Byzantine characters to pick up Byzantine traits. The triggers you posted are restricted to Byzantine characters and thus function as intended by the submod creators.
In order to give the Byz traits to only Byz characters in the four instances I cited, you'd need to add new triggers. For example:
Code:
;------------------------------------------
Trigger StandardBattle_CrushingVictory
WhenToTest PostBattle
Condition IsGeneral
and WonBattle
and BattleSuccess >= clear
and I_ConflictType Normal
and BattleOdds >= 0.25
and BattleOdds < 1.5
Affects GoodCommander 1 Chance 75
Affects Military_Edu 1 Chance 10
Affects Military_Career_In_Byzantium 1 Chance 100
as it stands would cause a character of any faction to get the Military_Career_In_Byzantium trait.
If you still want that chance for Byz, and only Byz characters, you'd need to do this:
Code:
;------------------------------------------
Trigger StandardBattle_CrushingVictory
WhenToTest PostBattle
Condition IsGeneral
and WonBattle
and BattleSuccess >= clear
and I_ConflictType Normal
and BattleOdds >= 0.25
and BattleOdds < 1.5
Affects GoodCommander 1 Chance 75
Affects Military_Edu 1 Chance 10
; Affects Military_Career_In_Byzantium 1 Chance 100
;------------------------------------------
Trigger StandardBattle_CrushingVictory_Byz
WhenToTest PostBattle
Condition IsGeneral
and WonBattle
and FactionType Byzantium
and BattleSuccess >= clear
and I_ConflictType Normal
and BattleOdds >= 0.25
and BattleOdds < 1.5
Affects Military_Career_In_Byzantium 1 Chance 100
Trigger Trigger StandardBattle_CrushingVictory would fire for all factions. Trigger Trigger StandardBattle_CrushingVictory_Byz would fire only for Byzantine characters.
Rinse and repeat for the other three and your fully back to the intent of the BtR team.