So I'm getting notifications that the two stylist roles are empty, but I have two stylists in my town. Does the mod not recognize them? The pop-up to fill the roles occurs very often.

Each stylist can only be assigned to one station. Do you have four stations (or more) in town? What are these two stylists actually doing if they aren't assigned to those two stations, have they maybe picked up other jobs?

When Register is set to disallow what it calls immigration, it can only use unemployed sims to fill unassigned roles. If there aren't any, then it has no one to assign to them and it gives up, displaying a warning. Do you have Register immigration switched off and does it need to be?

I have two stations in town, and none in any residence. MC demographics lists my two Sims as the two stylists. I have it set to ask me to fill the roles. Immigration is off since I'm controlling a 'story' that doesn't really allow for randoms..

Here is where one gets likely to confuse the Stylist Ambitions career with the Stylist Role Sims. I can't remember if the career sims are really assigned to a Stylist station on a community lot, the only one I ever played for a while did his styling thing wherever he felt like it (he, I mean I wasn't all that serious about progressing that one, he was pretty much a spoiled rich kid with nothing else to do). The Role Sims have to be assigned, otherwise they aren't stylists. That would sort of be like being a cashier without a cash register (no such thing).

So if you intend these two sims to be inactive Role Sims, can you not click on each of the two stations and use Register to assign them or does that not work or undo some other plan?

The career Stylist sims do use the Stylist Station at the Salon's that's one of the reason's Register will always leave at least 1 or 2 Stylist stations open by default or it should I've noticed that with Barneys Salon which has 4 stations but only gets 2 assigned to role sims and the other 2 are left open and I think you can change the number of how many stations get assigned to role sims in Register.

I think I see... So filling these roles wouldn't leave my Sims with nothing to do, it's like they're freelancers or something

There's this under Find Empty Roles in Register interactions: "Note: Only populate one stylist station and Tattoo chair per lot, even if multiples are listed." What's that about?

If your assigning manually that's for Roles if you have 3 Stylist Stations then only assign 1 to a homeless Role Sim and leave the other 2 open for residents in the Stylist Career to use but the Tattoo chair I'm a little unsure on as that's only for Role sims I think

Oh wait now I remember sims can raise their Tattoo hidden skill by using and giving other sims tattoo's by using an unassigned Tattoo Chair