I interpreted York saying she did turn off her syncing with Punk Records just for this one time and held back only the information that she stole part of the mother flame. But you are right, Oda could have also meant that she cut herself off from syncing altogether since then. Either way, in this case we still have the main problem of the Stellar knowing that the mother flame was used on Lulusia. Where did he get this information? It can't be Stussy, because she is not on the Stella's side. York even hints here that this is the case by wondering how Vegapunk knows this information, and therefore has to have intel from somewhere within the WG. If York was sure that Stussy was on Vegapunk's side, she would not have questioned the Stella's knowledge about Lulusia at all, but came to the conclusion that this source within the WG must have been Stussy.
It could have been Lucci or Kaku, who gave Vegapunk the information, since they did seem to know something about the "Lulusia incident" back in chapter 1062. But this is only theorie.