No. The main part that I think you are misunderstanding is that her powers were derived from a power source (the warp drive) made by the Tesseract, but not the Tesseract itself or even the Space Stone, just a source of power made by the Space Stone.
This is kinda similar to how the Maximoff twins gain their powers from Loki's specterscepter but still retain them perfectly fine even after Ultron breaks it open to acquire the Mind Stone from inside. In other words, the origin of a person's superpowers doesn't have to keep existing to be the source of the powers. Just like the radioactive spider doesn't have to stay alive forever for Spider-Man to keep swinging around.