The simplest process I can think of would be the disintegration of a nucleus into quark and lepton particles that have a total rest mass under about 10 MeV and an original kinetic energy of about 930 MeV.
... but it still has to get through the outer layers with enough of that energy to count ... you realize quarks don't exist by themselves. The closest you'll get is a quark-gluon plasma. So you still have trouble with Occam's razor here: why can't the jet come from the surface layers? You have the same amount of speculative hand waving and fewer obstacles.
One of the reasons for studying these things is that they are basically a really big nucleus ... held together by gravity mostly... so here we have the intersection of a QM object with a gravitational object. The intersection of QM and gravity remains a mystery so: very interesting.
Note: please do not use wikipedia as a starting point to formulating novel theories.
What you are doing is basically speculation. I think there are rules about speculation around someplace.
The short answer to your original question is "nobody knows: there is not enough information".
Why does this neutron star have a jet? Its moving at least 5 million mph so how can it be accreting? A young neutron star shedding excess mass might be an explanation. Does anybody have a suggestion?
5Mmph is a bit under 1% the speed of light, and 10x the speed of the Solar System. Why would traveling this fast mean it does not have a jet? Remember that all reference frames are equal, so, if it is OK for a stationary neutron star to jet, the same mechanism should work for a moving one. The article you cite does not seem to think the jet is at all unexpected.
Note: is 5 million mph fast? Sounds fast ... but it's an inconvenient number so let's convert a bit:
5000000mph is 1390mps, or 2360kmps, or 0.007c
Well it's not relativistic (##\gamma = 1.00002##)
To compare such slow objects, kmps (kilometer's per second) would normally be used.
(If you want to explore astrophysics more, you should get used to the metric system.)
The Solar system is traveling about 240kmps
The escape velocity of the Milky Way is 317kmps
The fastest star in the MIlky way, though, is doing: 1200kmps (2700000mph)
... so yes, that's pretty fast for a star.
But this should also give you a feel for the kinds of numbers to expect.