When any member of the Auxiliary is physically injured or dies as a result of physical injury incurred while performing any duty to which he has been assigned by competent Coast Guard authority, such member or his beneficiary shall be entitled to the same benefits provided for temporary members of the Reserve who suffer physical injury or death resulting from physical injury incurred incident to service. Members of the Auxiliary who incur physical injury or contract sickness or disease while performing any duty to which they have been assigned by competent Coast Guard authority shall be entitled to the same hospital treatment afforded members of the Coast Guard. The performance of a duty as the term is used in this section includes time engaged in traveling back and forth between the place of assigned duty and the permanent residence of a member of the Auxiliary.