They are referring to how California residents contribute more in federal tax dollars than they get back, making it a donor state. Florida gets more federal dollars than the residents contribute, which did surprise me, but it appears to be the case. However, it is not necessarily California residents subsidizing Florida. The residents of New York, New Jersey and Massachusetts all contribute a significantly greater positive balance in federal taxes than do residents of California.
The top donor states do vote blue, but I'm not certain this is a causal factor in the strength of their economy. The consistent donor states of Texas, New York, New Jersey, Massachusetts, Connecticut, and California have all had strong economies for the last century regardless of who has been in power.
Those donor states, except Texas, have strong economies because they're basically where smart people are concentrated: those states all have premier universities, and various industries (like tech in CA, pharma in NJ, finance in NY, etc.) that depend on highly-educated "knowledge workers". Texas is rich because of natural resources (energy) mainly.
Because smarter people have migrated to these states, they vote Blue, because the Red party these days is basically the party of anti-science, uneducated religious nuts. University graduates overwhelmingly vote Blue in the US. (Also, there's a high inverse correlation between education and religiosity.)
Keep in mind, it wasn't always this way: not that long ago, the Republican party was the party of fiscally-conservative pro-business and other upper-class people (and the Democratic party was the pro-labor and other generally lower-class party), so these states frequently swung Red. Not any more.
