If you are in southern California, I would like to refer you to the Western Region Supplement to the National Master Agreement:
http://teamster.org/upsupsf-contract-updates/ups-agreements-2013-2018
Specifically, Article 4 Section 1(c)-PROBATIONARY PERIOD (PART-TIME){page 183} & Article 5-SEASONAL PERIOD{page 184}.
Note that Article 5 defines seasonal employees as full time employees, which seems to imply that part time employees are not seasonal.
Call your Teamster Local & talk to the UPS Business Agent for your building, explain your situation, listen to what he or she has to say, and take notes of the conversation.
As far as the dues & fees you have paid, dues are required in a 'closed shop'; however, in my opinion, if in fact you don't end up making seniority as a permanent employee, you should ask about a refund of the initiation fee.