I used to be a housekeeper and my rate was $25/hour. I busted my ass for that though, and did detailed, move the furniture-type cleaning, every single time. For that price I would also organize their closets, cabinets, garage, buying the baskets and boxes myself. .
If you only pay $13/hour, you will get what you pay for. I have had cheap house cleaners myself, and the ones that didn't charge much, didn't DO much. My floors were still dirty, they never moved anything to clean under it, and I felt like I couldn't trust them either.
Please be very careful, some of these people are casing houses. They come and clean once and then a week or two later, you get robbed