You need to be on payroll and be an employee in S Carolina but you can actually work in Houston if they have a formal agreement between the two companies to allow you to work there. They are not the same company just because they are affiliated.
You must be on the payroll the E-Verify company. Your location does not matter.
Mr. Shusterman's (former INS Trial Attorney, 1976-82) response to your question is general in nature, as not all the facts are known to him. You should retain an attorney experienced in immigration law to review all the facts in your case in order to receive advice specific to your case. Mr. Shusterman's statement above does not create an attorney/client relationship.
As long as you are on the payroll of an E-verify employer, your actual physical location is irrelevant.
Kindly be advised that the answer above is only general in nature cannot be construed as legal advice, given that not enough facts are known. It is your responsibility to retain a lawyer to analyze the facts specific to your particular situation in order to give you specific advice. Specific answers will require cognizance of all pertinent facts about your case. Any answers offered on Avvo are of a general nature only, and are not meant to create an attorney-client relationship.