So the primer bulb that was on there was the solid one that's more domed and the one you needed to replace it with was the one that is less domed and has a small hole in the middle.
That is a common problem and prevents the fuel from being sucked up the main jet and through the emulsion tube or whatever you want to call it.
I think basically what is going on is it creates a vacuum and it can't suck it up without the whole event because on those mowers if you lightly take your finger and cover the hole once the running properly they will start to stutter and die out..