It's not an immigration fee as you pay it when you have to leave the Philippines (so mostly when emigrating...).
If settled abroad, you pay P200 exemption fee instead of the P1620 travel tax.
By Law, all Filipino citizen are required to pay the travel tax unless they can benefit of the travel text exemption (fee is P200 in this case).
Everything is explained here: http://www.philtourism.gov.ph/ttax.html
If the airline let her board the plane directly with your eticket, this mean you already paid it (look at the tax details on the e-ticket). If not they refuse the check-in and send you to pay it at the Travel Tax desk in the terminal.