I'd suggest still completing daily water changes, twice daily if possible, with the breeder box. Those things don't nearly have the flow that you'd want to be completely reliant on the openings.
But, simply slowly pouring water from the tank into the breeder box should be more than sufficient. If you don't want to do that... you can also just suck water out of the breeder box with the turkey baster and return it to the main tank... this would draw more water from the main tank into the breeder box.
I say that because you'd be surprised how little actual water is transferred during the course of the day through most breeders.