How can one catch the real "piso fare deals" from airlines? Felt like I'm not so good at it even though I frequently check their notifications through email or FB ads. Do they really exist?

Sign up on their websites. They regularly email newsletters and announcements about their upcoming promos. Based on a personal experience, as a regular piso fare abanger, I mark the date of the start of the promo and wait until 12 midnight. Expect heavy traffic on the website because people are really buying for the piso fares so patience is really a virtue.