I bought something that's in Cali and I live in Fl. They said the anticipated ship date was: Wed 10/09/2013 10:00 pm. Do they mean California time or Florida time?

Generally speaking, the delivery time should be in local time. I suggest this based on what usually happens with air travel across time zones: Tickets tend to display the local landing time so as to facilitate people's plans for onward journeys.

I'd assume a similar thing would happen with delivery services.

However, to be on the safe side I'd recommend double checking with the courier service making the delivery.

In my experience, they won't hesitate to leave your item at the depot and ask you to collect it if you aren't home at the time.