Only flights ticketed and operated by Aer Lingus earn any tier credits in Aer Club. Had you booked the flights through Aer Lingus either online or through an agent you would have earned on tier credits/avios on 3 legs (MAN-JFK, EWR-DUB, DUB-MAN) and avios on PIT-EWR
Flights operated by United earn points but not tier credits under a long standing partnership
Once Aer Lingus joins the AA/BA/IB joint venture fully these flights should earn, however thats the future not present