“Not necessarily. If a woman converts to Judaism; promising to keep the 613 mitzvot and does so sufficiently as a frum Jew, and has children; then her children are Jewish.”
What DY meant was: if her conversion was acceptable and she is Jewish, then her children are Jewish as well. If her conversion was not acceptable and she is not Jewish, then her children are not Jewish.
Basically, her kids are whatever she is. You had seemed to imply that it’s possible for her to be a non-Jew and yet for her kids to be Jewish. That is what DY was responding to.