I am a Filipino Citizen traveling to Mexico, I learned that I can save more if I buy ticket from Manila going to Tokyo and then buy a roundtrip ticket from Tokyo to Mexico and vice versa so technically, I'll buy two separate flight tickets from Manila to Tokyo and then Tokyo to Manila. Is it still considered transit if I'm traveling the same day just different flights and tickets?
If the two airlines you are flying have an interline agreement and allow you to check your baggage through to the final destination, you would be considered a transit passenger. If they do not, then you have to reclaim your bags and recheck them, requiring you to go through immigration and be subject to visa rules for Philippine nationals.
Your best bet is to call the airline you leave Manila on to see if they can check your bags through to the next carrier.
If you can check your bags through, you will need some proof of your next flight, as that is checked before you are allowed through security screening at Narita. The best proof is your next boarding pass. But as you are traveling on different carriers, you can usually show a printed copy of your e-Ticket for the next leg. Once you have cleared security you can go to the transit desks to get your next boarding pass.