I don't know why but the agents that initially opened the line keep insisted that they could not cancel the reservation ( maybe because of the multi-city ticket ) and my process involved speaking with that department that handles refunds.

However, the issue was solved and now, I have a refund identifier where I could track the progress of my refund online.
Also, I have double checked that my ticket was cancelled and when I log in to my reservation with the PNR, all segments were removed so most likely they did cancel my ticket.

I hope that it doesn't take that long for TP to credit back the refund. I'll wait and see.

By the way, I was polite to all agents that I spoke despite the high wait time so that "pesky customer" term would not apply to me. I am not one of those who shout at the agents when I wait for a longer time or when they don't get my job done.