First, you are aware that depending on the contract, you have to file a schedule C when you are working as an independent contractor and you can deduct your expenses; when you are a W-2 worker, you can't deduct expenses. And if you have common expenses, you have to allocate them and can only deduct the percentage equal to your schedule C work, ok?
Now as a general rule, most states only tax you if physically live or work in that state while you are performing your duties. That means that if you are sent to Kansas, for example, you will owe Kansas income tax on income you earn while working or living in the state of Kansas. If you performed half your duties for that company while physically in Kansas and half from your home, you would report 50% of income from that job as Kansas income. You would use a non-resident return since you are not a resident of Kansas. (You may end up filing a lot of non-resident returns if you work in a lot of states.) You need to keep track of days worked in each location so you can allocate your earnings correctly.
There are always exceptions to the rule. For California, for example, if you are a W-2 employee, your income is only considered California income if you physically live or work in the state of California while performing the work. But if you are a freelancer, you have California-source income if your clients or customers are located in California even if you never set foot in the state.
Seven states have a "convenience of the employer" rule. They are Arkansas, Delaware, Nebraska, New York, Pennsylvania, Connecticut, and New Jersey. This rule states that if you work out of state for the convenience of the employer, your wages are not considered state wages. But if you work out of state for your own convenience, your wages are considered state wages and you must file a non-resident tax return. This is complicated by the fact that your employer is an agency in Florida, and not the company you work at temporarily. So I think this means that when you are working as a W-2 employee, you can ignore the convenience of the employer rule, even if you are sent out to work for a company in one of those states. But I am not 100% certain of that. The convenience of the employer rule usually does not apply to freelancers (although see California's take on the subject) but you may want to review this when you get offered each new assignment.
As you can see, the issue is complex and I have only covered the basics as I understand them. You may want to consult with a tax advisor. You can certainly start with the agency and ask if they have advice or information handouts or some other guidance or an expert you can talk to.
Record keeping is your friend here. What days did you perform what jobs, whether they were freelance or W-2, and where were you physically located.
