The canton migrations office decide your permit based on work contract type and quotas - not employer, not agent, not you.

I'll repeat, because it is so simple, permit is nothing to do with employer or agent despite what any agent may say...

If you are British etc:
You arrive in Switzerland, maybe start work first, maybe not, but go the local Gemeinde/Kreisbüro (local government office) within 8 days and register.