Yes, not only do you need to pay the difference but you'll also have to increase their monthly payment. Otherwise they'll look for someone else who can afford their services or worse, might mutiny.

I will provide NPC's who do actually have class levels, hirlings and cohorts are simply NPC's who you can straight up pay for. The NPC's with class levels are generally more unique in character design (Because I'll create them from scratch as oppose to just slapping a race onto an NPC class) and may have different requirements to obtain/keep them.