Here is a proper explanation of entanglement across time:. 2 photons are entangled that have never existed at the same time. It is the source for one of the diagrams in the article you mention, and in fact is the original basis for the article.
https://arxiv.org/abs/1209.4191
"The role of the timing and order of quantum measurements is not just a fundamental question of quantum mechanics, but also a puzzling one. Any part of a quantum system that has finished evolving, can be measured immediately or saved for later, without affecting the final results, regardless of the continued evolution of the rest of the system. In addition, the non-locality of quantum mechanics, as manifested by entanglement, does not apply only to particles with spatial separation, but also with temporal separation. Here we demonstrate these principles by generating and fully characterizing an entangled pair of photons that never coexisted. Using entanglement swapping between two temporally separated photon pairs we entangle one photon from the first pair with another photon from the second pair. The first photon was detected even before the other was created. The observed quantum correlations manifest the non-locality of quantum mechanics in spacetime."
Note that entanglement across space and time is usually called "quantum non-locality" even though there can be a temporal component. Yes, quantum nonlocality operates somewhat differently than would be expected by classical or Einsteinian spacetime. However, there is no direct conflict (as their applicable domains are sufficiently different); and entanglement follows the normal rules of QM. Those rules have been around for about 90 years, and in fact Einstein co-authored a famous paper (nicknamed EPR) about entanglement in 1935.