Not always. Most employers will likely realize the differences in cost of living and try to get you relative to your local market. One of the benefits of remote employees for an employer is around being more cost effective.

I've also been in the situation working for a remote employee who tried to pay comparable CA wages (wasn't in the Bay Area), but didn't understand the true cost of living differences. Also been on the flip side, in office in SF and looking for people in cheaper markets.