Hmm, that's not how I read it (though I still haven't gotten around to reading the paper, so please let me know if I'm going off-track). It sounds like the bubbles are *created* by the electrons as they enter the fluid - no electrons equals no electrostatic repulsion field repelling the surrounding helium equals no bubble. And it's not that the paths through the liquid have different wavefunctions, it's that fractional wavefunctions created when an electron is partially reflected from the liquid's surface create smaller, faster bubbles than those containing a "whole" electron. Perhaps the wavefunction is splitting even further within the fluid, forming multiple even smaller bubbles, but I would think that the same electrostatic repulsion that creates a bubble in the helium would also tend to constrain the electron near it's center. It could be though that splitting due to "escapees" is responsible for the rarer apparent continuous spectrum of speeds.
Given the speculation that at least some of the "bubbles" might be due to ion contamination, I suspect they're probably directly measuring charges reaching the detector, rather than the bubbles directly - if you could directly detect the tiny bubble created by a single electron then you could probably also detect that there was a massive ion in it rather than an essentially sizeless, massless electron. So if you've got 10 "1/2 wavefunction" bubbles formed at the surface then all ten reach the detector ahead of schedule, but only five (on average) will actually be detected, with the remaining five electrons collapsing into having been reflected at the surface.
And yes, that would mean that you presumably get bubbles formed and sustained by electrons that "weren't there" - that would seem to be the natural corollary to having bubbles being formed by an impossibly small charge that "couldn't" be there. What appears to me to be so revolutionary about this experiment (assuming it's being properly interpreted) is that for the first time we're observing a situation where you can't construct a coherent classical description of the path of a single particle. In every previous case, while we could detect quantum wavefunctions in the distribution of results, each individual detection still corresponded to a valid classical path.