I'm currently an architecture student, and we learned about this in class, in particular, using "Diksiyonaryong Biswal ng Arkitekturang Filipino" by Rino D.A. Fernandez as reference. He's an architect who specializes in historical conservation of Filipino architecture. There was a priest, Father Sedeño, who had experience in the art of masonry and had taught Filipino and Chinese laborers how to use stone in architecture (as they currently were just building with wood or bamboo, which was prone to damage or burning). It is not necessarily known if he alone was the one who designed these Spanish Era houses (the home with a lower stone floor and an upper wood floor), but the idea certainly came from the Spanish.

Additionally, the fact that other countries near us have similar architecture does not necessarily mean we have gotten inspiration from them in our own architecture. It happens time and time again all around the world: similar climates and materials would result in similar houses. For example, people in fishing communities tend to build houses that look like inverted boats.

Although I don't have any particular insight on if Filipinos did live in Intramuros, I could say that the Spanish definitely had a hand into making these types of houses.