This is not a game/job mechanic but a memory-saving dev technique that they chose to use to reduce the number of cooldowns being tracked at any given time. In general, it won't matter and isn't worth mentioning because if you change jobs and then enter a duty, all your cooldowns reset; and in other situations where you might change jobs--maybe between FATEs, for example--the loss of one or two cooldowns for a few seconds to two minutes won't make a meaningful difference.