But that's not what it says, it literally says 'we have a Filipino woman, who works for us'. The difference is subtle and that's what made it jump out at me. If it were written the way you just did that likely would not have happened. I assume this is because this isn't my first language even though I use English more than Dutch these days but oddities like that jump out at me likely much more pronounced than they would to someone who is born into the language.

If I had written something to the same effect it would likely have been 'A Filipino woman who works for us' just to avoid that sense of possession, doubly so because of the context.