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Character Config -> Chat Settings (the bottom one) -> Pick the offending tab at the bottom -> Go to the Battle tab (I think) -> Pick and choose what is displayed.
I'm assuming that this happens in Crystal Tower, and all the buffs of everyone in the Alliance are turned on by default. To fix this in particular, change the dropdown from 'You' to 'Alliance' and uncheck all the boxes.
Note: Not in game ATM, so specific details may be different.
DiZ: Will you take the path to the light or the dark? Riku: Neither, I choose the path in between, the path to twilight.