I have been a Florida resident for 45 years now and have worked in plenty of states. I agree that you will most likely have to pay state income taxes in the states you have worked. Especially if Robert Half deducts your estimated taxes from your paycheck and pays worker's comp in each state. You will have to file tax returns simply to get a potential refund of the deducted taxes you will be paying every week.
In my case, I worked for 3 years for a company headquartered in North Carolina and they paid me no matter what state I was working in. Although they never deducted income taxes from my paycheck, NC made me file an income tax and prorate my total income by the number of nights I stayed in North Carolina.
The individual tax codes are very complex. Just imagine being a pro athlete and paying your taxes in each state. Take a look at this
Forbes article on state taxes.
