That's because you didn't drain the cyst, you cured it. Draining the cyst involves going to the incubator and breeding a Helminth Charger, but curing it by sitting in the chair completely inoculates the Warframe from the cyst.
I just reread the Helminth info and I understand that my nidus must have been infected by another nidus or infected warframe and gotten the cyst before I entered the room which would have cured it is my understanding of what happened. I also read that Nidus can get a cyst from entering the room i'm guessing if he doesn't already have one and it'll mature after a week, would going back into the room once the cyst matures cure him from getting another cyst?
Because your Nidus was infected from another player and not by sitting in the chair initially, you might be able to reinfect him if you sit in the chair again. However, from my experience, once I cured my Nidus the context action to sit back in the chair did not appear, so I could not reinfect him.
If you cannot reinfect him you have a couple of options.
Either way you're not at a total loss for getting the Charger.