Self Employed paid - Who do I owe?

I am a contract worker.  I can work as a 1099 or a W-2 depending on the contract that is offered.  I am hired by an agency who is hired by another company.  My pay, 1099 or W-2,  always come from the agency which is located in Florida.  I am also a Florida resident.  The companies that hire the agency can be from any state for example California.  Sometimes they want me to go to the company that needs me and sometimes I work from my home.  The company never employs me or pays me.  They pay the agency and the agency takes their cut then they pay me.

 

My question is am I required to pay state taxes to the states where the companies are located that hires the agency ?  Since they never employee me or pay me am I responsible to pay other states taxes?