I'm not a physicist, only an engineer with interest in physics. Correct me if I'm wrong with this.

The electron ebbing in and out of existence around the nuclues is not a mystery as far as I know. This mechanism is basically the same as with virtual particles that also pops in and out of existence.

The layman explanation would be something like this. Each particle is an excitation in a particular quantum field (and there are many quantum fields, one for each type of elementary particle). This quantum field permeates all the 3d space around us and inside us. Now, imagine for a moment that this particular quantum field is 2d instead of 3d, imagine it like an infinite piece of cloth. A wavy cloth rippling in all directions. You'll observe wave peaks and as well as wave troughs. Some wave peaks are high. Some wave peaks are low. A wave peak in that field only manifests as a particle if its amplitude reaches a certain threshhold. So not all wave peaks are particles, only those that are high enough. But like I said, the cloth is wavy. What's a wave peak now can become a wave trough in a zillionth of second. And a wave trough can become a wave peak just as fast. The decrease in amplitude in one point in space contributes to the increase of amplitude in another nearby point in space (conservation in energy). And that's basically it. The electron exist at this one point one time but the the excitation decreases in amplitude at that point of space which contributes to the increase of excitation at another point, resulting in the electron manifesting itself again, like it popped out then popped in again of existence. In our imaginary 2d cloth, the rules of the quantum world makes the electron circle around the nucleus (and this nucleus are excitations themselves in other parallel cloths or quantum fields). It is easy for us to imagine how such particle would circle in a cloth. Just imagine it doing a merry go round. But that is 2d. In reality the quantum field is in 3d. Try imagining how that encircling mechanism will work in 3d. It's not like a satellite orbiting a planet, where the satellite follows a straight direction. The waves in the quantum field ripples in all directions. So the electron can popped in and popped out of existence anywhere in the shell surrounding the nucleus. And that's what we call the electron cloud.

The cloth analogy I used is an oversimplification btw. In reality the electron is a manifestation of many wave peaks (not just one peak). The amplitude of each peak represents a probability of detection of the electron (the probabilistic nature of the quantum world).

So yes, the ebbing in and out of existence of an electron is not mystery. The only intriguing part what they said is the past-ahead-of-the-future stuff. But not until they give a more detailed description of that theory, we can't really make anything out of it.