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Yes, when you join an army you cause their cohesion to drop faster but it effects at most only 1 per day (if there is no special case).
Probably army leader made cohesion boost at your second try, this means his clan has enough influence but he did not boost at your first playthrough. Maybe when you join army its cohesion boost cost increased and his influence was at just limit. I will examine your save and give you answers. Also if you look code there is random factor there. So maybe it is because that random.