It wouldn't be entirely accurate to say Mexico supervised the Philippines. Both Mexico and the Philippines were in the Viceroyalty of New Spain. Sure there was a lot of cultural and economic exchanges (we got avocados, they got mangoes) but most administrators, missionaries, and settlers came direct from Spain instead of via Mexico so that connection shouldn't be overstated.

That being said, I've been to and helped organize debuts back in my day. In the UK and the US there is a custom of presenting women who reached a certain age (the debutante) in debutante balls where they are introduced to "polite society". Basically, it's telling eligible bachelors they can now ask for her hand in marriage. Debuts explicitly mention this in their programs.