Labor only contractor

Dear PAO,

My friend and I work for a manufacturing company. However, we get our salaries from the agency that recruited and hired us. During our tenure, we filed a labor case for underpayment of wages, which we suppose is why we were asked to no longer report for work the following week. We filed for an illegal dismissal case against our agency and the manufacturing company since we feel that they are our true employers. Truth be told, aside from the payment of wages, everything else is done by the manufacturing company. They tell us how to do our work and provide the equipment for us, and we ask permission to file our respective leaves with the manufacturing corporation. Is the manufacturing corporation our true employer?