Personnel detailed under subsections (b) and (c) of this section shall be paid from applicable appropriations of the Service, except that, in accordance with regulations such personnel may be placed on leave without pay and paid by the State, subdivision, or institution to which they are detailed. In the case of detail of personnel under subsections (b) or (c) of this section to be paid from applicable Service appropriations, the Secretary may condition such detail on an agreement by the State, subdivision, or institution concerned that such State, subdivision, or institution concerned shall reimburse the United States for the amount of such payments made by the Service. The services of personnel while detailed pursuant to this section shall be considered as having been performed in the Service for purposes of the computation of basic pay, promotion, retirement, compensation for injury or death, and the benefits provided by section
213 of this title.