I would believe that they were immediately buried in the local cemetery, see Paul Warren Brown's previous input above.

Inasmuch as the surviving family members hired attorneys to file claim for their pay, allowance, effects, etc., there is a good possibility that they were reburied at home.

For information on this subject:

08 22 1862 [Friday]

Appearing in the Athens [Tenn.] Post of this date:

Exhumation of Corpses.

Our attention has been called to the fact, that a number of instances, the remains of deceased soldiers killed in the recent battles, or the victurms of disease, have been disinterred for transportation to their late homes, at remote distances from Richmond. When a metalic burial case can be obtained, this transporation may be effected; but otherwise, the expenditure for a wooden coffin, with sawdust or other packing, is just so much money thrown away, if we are correctly informed. We learn that it is rarely the case a corpse forwarded in this way reaches its destination. The rapididty of decomposition impels the railroad authorities to remove the corpse from the train, for re-interment, and thus the anxiety of relatives and friends to secure the remains for burial is defeated, and the heavy expense incurred in providing the coffin, etc., rendered unavailing. The removal of corpses should be deferred until the return of cold weather. - Richmond Whig.