Here's more info about hiring domestic help. As Stevesolar said, it's illegal to hire domestic help from others than an official agency. Some people aren't familiar with the laws and/or don't care but the consequences can be severe if caught.
I can recommend Twinkle Time. They have been providing reliable service for me for over four years now. You can request to have the same maid if you book a regular slot. They have at least two who are good with cats.
When hiring an agency maid you pay the hourly rate, the agency pays the maid's salary and accommodation as well as insurance. I tip each week and I think that's ensured that I get a consistent good service.
I would recommend to be present at least the first time to instruct the maid what you want doing and how you want it done if you're particular about something.