The delta with star has been used for all of Starfleet in the nuTrek movies, which are set during the TOS era. The delta itself was used as the uniform emblem for both the Kelvin and the Franklin, which were in service prior to the incident which split the universes into oldTrek and nuTrek.
So, the simple answer is this: the delta shield with star has been the emblem associated with Star Trek as a whole for nearly half a century and, just like bumpy-headed Klingons, is now treated as always having been the symbol of Starfleet. It does not require explanation any more than the Klingons did.