Answer:
Great question. Well, let's start of with this. Filipinos, are descended from China. From China's Yunna Province, same place of origins as Vietnamese, Malays, Cambodians and a lot of Southeast Asian people. So they brought the Chinese traditions with them. Also, pre-colonial Philippines has owed a lot of contact with Chinese merchants and traders who introduced Chinese culture to the Philippines. I can't exactly remember if the Chinese had any territory in the Philippines. But I was told, there's a museum in China that contains the first non-Chinese ruler. Who was from the Philippines. Chinese culture also influenced the cuisine of the Philippines. Lumpiang shangai, is based off of Chinese egg rolls. But smaller and deep fried longer and contains more meat than the traditional Chinese egg rolls. Balut, which is fertilized chicken egg was brought over by Chinese merchants. Sao pao, steamed-buns with sweet pork or chicken is also Filipino food, as it is Chinese. In fact, back in the Philippines my dad's officemates would always made and bring these bad boys over to work and share it with us. Sao mai (dumplings) are Filipino food as well as Chinese.
Chinese also brought in Buddhist in the Philippines. The ancient Filipinos and ancient Malays were both Buddhists and Animists. Before becoming converted to Islam and then Catholicism (for Filipinos).