Immediately upon the passage of this act, the Adjutant General shall ascertain the individuals who are veterans, as defined in section two, and, as to each veteran, the number of months of service, as defined in section three, for which he or she is entitled to receive compensation, and his decisions shall be final and not subject to review by any court or by any other officer. In all cases not within the express purview of this act, the decision of the Adjutant General as to payment or nonpayment of compensation or eligibility therefor shall be in all things final.