How do unemployment benefits work when you move to a new state for the same employer?

I have questions about CA unemployment benefits eligibility that I’m not able to figure out from the website.

In preparation of moving to East Cost location of my office, I had moved my address to office FL starting from June 15 20. I have been paying CA tax until June 15, 2020. Considering better unemployment benefits in CA when my employer fire me on July 31 2020, I asked them to move my office address back to CA so my 31 July paycheck was in CA. They are saying they would continue my payroll until October for severance.

Do you think this brief switch to FL would be a problem while claiming unemployment? In short, does one need a continuous presence to qualify for unemployment benefits, or it’s more like a bucket you contribute to over time and if you have been present for 6 months you get the benefits?

If this switch doesn’t create problem, should I ask them to pay me severance in one go in CA so I can start my unemployment benefits sooner?