different answer for specialists and drillers.
if you tap a specialist you will see a stay/go button in their info panel. by default, specialists GO with any sub that passes through or launches from their outpost. they also keep going with whatever sub they're on. if you tap the the stay/go button and set the specialist to STAY, the specialist will stay at its outpost when a sub passes through. if the specialist is aboard a sub and you set it to STAY, it will stay at the next outpost that the sub passes through.
for drillers there is no way to do this yet. one of the features we have planned is queueing up future orders. that means you can use the time dial to scrub forward into the future and then issue a command there in the same way you do normally. so you'll be able to go to the time when the sub arrives and then launch a new sub and load it up exactly how you want it.