It has little to do with that. If that were the case, Florida would not have been within spitting distance of California. Why is New York at the top of list? They had a similar response as California.
The issue is far more complex than "taking things seriously". Population density, climate, age of population, and job types probably contribute more than simply "taking things seriously".
The Federal Government cannot restrict citizens from traveling between the states. I don't know anyone, here in the US anyway, who would even suggest such an action.
The privileges and immunities clause, Article IV, Section 2, Clause 1 of the United States Constitution, protects the interstate travel rights of US citizens.
In fact travel rights were actually restricted in practice by the Federal Government and it's agencies, and states under both Republican and Democrat leadership. There are many well established exceptions that restrict access to constitutional rights under various circumstances, so the contention that this can't be done falls a bit flat. If nobody can do it, how come everybody did it?
https://www.worldometers.info/coronavirus/country/us
I'll let it speak for itself.
https://www.statista.com/statistics/1109011/coronavirus-covi...
If states were countries, half of the top 20 per capita would consist of US States, with the other half essentially being developing nations.
In fact, I'd say that the only reason the US per capita rate is as low as it is is that states like California (itself accounting for over a tenth of the population) actually took things seriously and brought down that average.
Split hairs all you want, but the fact that the US at one point accounted for a quarter of all cases despite being 4% of the world's population is a stain on the whole country, and a significant argument that the US is directly to blame for the pandemic lasting as long as it did.