Round shields are far less common in the Philippines, most tribes from back to the arrival of the Spaniards being recorded as carrying the tall, narrow kalasag instead. The round shield is called Tamin in parts of Mindanao, but elsewhere it is also known as Palisay.
Now I’d always thought that Palisay was a local word, until while browsing an article on Sinhalese arms and armor I came across a very surprising detail: they called their round shields Palisa. Further research revealed a bunch of other very similar names: Phari in Northern India, Paliha in South India, Perisai in Sumatra. They all referred to a round shield, often of wicker, with a central boss; as one goes south, additional bosses are added around the center to form the pattern you see at top.
I’ve seen shields both with and without the bosses here. The boss-less shields are usually of carved wood coming from the Sulu and Maguindanao areas. There are also wicker ones, both with and without brass bosses; and a few entirely of brass, with very ornamental bosses in the form of six- or eight-pointed stars, or other symmetrical polygons often seen in Islamic art.
I think this gives a clue as to where the Palisa came from. The word itself is very likely Indian, given the spread of the term across various Indian languages down to Ceylon. The predominance of Islamic motifs and the almost exclusive use by Muslim tribes tells me the most likely source of this shield design: it came from our west, that is across the Indian Ocean, brought by Indian and Arab traders, likely adopted in Malacca, and from there to Mindanao.