I have read several article that says my cacti should be dormant in winter but I don't know if that rule applies here in the Philippines. We don't experience winter here in the Philippines and temperature here doesn't drop dramatically Should I still give my plants a dormancy period?
Probably not. There are growers here in Northern Europe who keep a small number of cacti growing under artificial light in winter, and they grow and flower as they are supposed to do. The main reasons why most growers in temperate climates let them rest in winter are: It is too dark and cold, and the cost for maintaining adequate light and heat by artificial means is too high. Cacti tolerate it, as they are adapted to long periods of drought in nature.
So does this mean I could still water my cacti weekly and expose them to direct sunlight even in the winter months?
Here in the Philippines we only two season that is wet and dry. But in the winter months, the southwest monsoon that brings humid wind changes to the northwest monsoon that brings dry but cooler winds to the coumtry.
I looked at some climate data, and your winters are hotter (and dryer) than our summers, and with a greater solar angle. I would definitely try to keep them growing through winter, especially since they look so dry. Once they have grown better root systems and taken up water you can experiment with them, like attempting to force them into dormancy (by not watering them) if they grow too fast or refuse to flower. As said, I think they will be fine without dormancy periods.