Going into a Swiss hospital using an insurance that isn't actually "swiss" (frontaliers for example) usually required you to produce a certificate from the insurance company saying that they'll cover you up to *"% CHF.
If it's an emergency admission they'll ask that you provide a certificate as soon as possible.
Sometimes you'll need permission from the company to arrange treatment in Switzerland as certain things aren't covered (or only partially covered), dental work for example.
In the case of doctors, pharmacy bills etc. you normally pay them when you get the bill, submit the bill to the insurance and wait to be reimbursed.
If you're using BUPA or some other similar company, wouldn't they be able to tell you if you can continue using their cover?