(Thanks to David Nishimura for figuring all this out! Here is the link to his article on this, which I am only describing below in my own words. https://vintagepensblog.blogspot.com/2021/10/the-original-mabie-todd-bulb-filler.html) In practice on the user end, there is no difference between this and a standard bulb filler. However, the bulb is attached to a device that is designed to guide the air flow out the breather tube, but refill the bulb with air remaining in the barrel. The breather tube is attached to the diaphragm housing. When the bulb is pressed, the diaphragm will move down to cover the holes to the barrel, and only leave open the central hole to the breather tube. When the bulb is released, the air flow will pull the diaphragm up, uncovering the holes to the inside of the barrel. If this functions correctly, the repeated action on the bulb will draw air from the barrel into the bulb, and expel it via the breather tube and out the nib end. In practice, a standard bulb filler is efficient enough that this is an interesting, but not helpful variation.
This appears to be the Riesenberg patent US1037660A – Fountain-pen. – Google Patents