I have not found any clue of how Minkowski would have explained the obvious fact -- that Poincare was not mentioned in his Cologne lecture Space and Time. Minkowski was certainly aware of Poincare’s paper Sur la dynamique de l’´electron published in 1906 (but received by Rendiconti del Circolo matematico Rendiconti del Circolo di Palermo on July 23, 1905) since he quoted it in his previous lectures given in November and December 1907. In his paper Poincare first published the important result that the Lorentz transformations had a geometric interpretation as rotations in what he seemed to have regarded as an abstract four-dimensional space with time as the fourth dimension.41Everyone agrees that Poincare made the discoveries and published them first, that Einstein and Minkowski knew about it but refused to credit Poincare.
Here are two attempts to explain Minkowski’s omission to mention Poincare’s paper in his Cologne lecture. ...
I think one should also ask why in 1946 in his Autobiography44 (as quoted in Section 2) Einstein wrote that Minkowski "showed that the Lorentz transformation [...] is nothing but a rotation of the coordinate system in the four-dimensional space." It seems Einstein was either unaware in 1946 (which is highly unlikely) of the fact that it was Poincare who first published that result, or he knew (perhaps from Born) that Minkowski independently had made the same discovery.
One can speculate that Minkowski might have independently made the discoveries before Poincare, but that does not help the reputations of Einstein and Minkowski. If Einstein thought that Minkowski and Poincare independently made the same discovery, he could have just said so. If Minkowski wanted to claim priority over Poincare, he could have put in a footnote saying "this fact was also discovered by Poincare" or something like that.
No, the only possibilities are: (1) Einstein and Minkowski did not understand Poincare's papers (in which case they did not understand the core of relativity), (2) Einstein and Minkowski were egotistically trying to hog all the credit for themselves, or (3) Einstein and Minkowski had some other beef with Poincare, and maliciously tried to cheat him out of the credit.
There are scholars today who have some bizarre quibble with Poincare's philosophy, and justify denying him credit for that reason, so reason (3) is possible. But the honest thing is still to credit him with what he published.
Einstein systematically lied about the origin of relativity from 1905 to 1946 and later.
I had a reader argue that Einstein should get credit for gravitational waves, even tho he first had the idea about 10 years after Poincare published the idea. The argument was mainly that Einstein knew that the waves had to be Ricci-flat, but then Einstein got that from Grossmann and Hilbert.