While it might be possible to create systems that "by the formal definition of the Kelvin scale is a few billionths of a degree Kelvin below absolute zero", you'll note that these systems are not colder than absolute zero. The article clearly states:
But don't be confused. The below-absolute-zero system is not cold. It is in fact very, very hot -- hotter than any positive Kelvin system.
The issue is that, "In cooler positive temperature systems, the numbers of particles in low-energy states outnumber those in high-energy states, giving rise to the formal quantum mechanics definition of temperature."
However in the system described, ". . . the entropy actually decreases as the system energy (and "heat") increase, giving rise to a negative quantum temperature."