The answer would have been as simple as: obviously national anthem first, then invocation..
Almost all programs, trainings & seminars I've attended; after the prayer, the emcee will tell the people to remain standing for the singing of the Philippine national anthem (gusto ko sanang magreact pero deadma na lang, hehe.. kasi alam ko na ang sasabihin nila.. Honor God first before anything.. that should always be the case..)
Even the Vatican City State has a national anthem, and the Pope stands at attention at the playing of the anthem of his state with that of any state he happens to visit, and only afterwards proceeds to invoke God and bless the people, after the state rituals have been concluded. READ MORE HERE
This is the way things should be and here's the proof:
Education Secretary Br. Armin Luistro FSC also reiterated the protocol of singing the National Anthem first before prayers in official programs. "We cannot call on God unless we gather first as a nation. The singing of the ‘Lupang Hinirang’ brings us together, and then we pray as one, even as we come from different traditions," he explained. READ MORE HERE
FROM RESPECTED ANON: Personally, National Anthem should precede just because it is more universal than many religions in the country and as it is a students/teachers meet/seminar/ program/training, you are surely going to have students/ teachers from different religions of the country as participants.