Except as hereinafter provided, appeals from a claims adjudicator shall be taken to a Referee. Whenever a “determination” of a claims adjudicator involves a decision as to eligibility under Section 604, appeals shall be taken to the Director or his representative designated for such purpose. Unless the claimant or any other party entitled to notice of the claims adjudicator’s “finding” or “determination,” as the case may be, or the Director, within 30 calendar days after the delivery of the claims adjudicator’s notification of such “finding” or “determination,” or within 30 calendar days after such notification was mailed to his last known address, files an appeal therefrom, such “finding” or “determination” shall be final as to all parties given notice thereof.