Unfortunately you're not missing anything.
I think the order in which they show in the list on the fleet command terminal is based on the order in which you recruited them to work for you. So, the first-listed Payload Specialist (for example) would always be the first listed one, etc. So you can know the first listed one is on, perhaps, your first listed ship, the second one on the second ship, etc.
Granted, assuming that is true, it could be thrown off if something happens to knock one of them out of your crew pool. Say the first one leaves your employ, now the "second" one is "first."
I think kinggath said on a stream not long after WT launched that they are still hoping to be able to ultimately use the vanilla assignment screen to assign to fleet ships but they haven't been able to make that work yet.