Manila Self-Transfer: Is 4 Hours Sufficient

Hello! I am planning to travel to Hong Kong via Manila this summer (mid July to early August). The cheapest fares I could find were: Arriving around 5:55am in Manila (UA189), 4 hours and 50 minutes to late morning 10:50am departure (CX906); while the return flight would land at around 4:30pm (CX919), 4 hours and 50 minutes again, 9:20pm departure (UA810).

The tickets would require self-transfer, i.e. having to pass through immigration, get my check-in luggage (which would be plenty, as I am travelling with others), pass through customs, immediately turn around and check-in, and pass through security. It would be done on separate tickets and airlines, which means if one delays, the other would not be available for compensation. Therefore, I would like to inquire whether 4 hours and 50 minutes would be enough for a self-transfer.

Both flights arrive and depart from Terminal 3. I would arrive from the U.S. on United, and transfer to Cathay Pacific, and vice versa. I am travelling on Business for the United leg, but I booked economy for Cathay, so no priority check-in. Read from some reviews that Manila airport is incredibly inefficient and chaotic, so just wanted to keep in mind the time.

In addition, when entering the Philippines, should I state that my purpose of entering is for "transfer", or should I say something else to ensure a smooth transfer, like "tourism"?

Thank you!