Tia developed a containment plan for Ayumi and her newfound abilities. In fact, she perfectly mapped out a plot of stars that were ideal candidates for Ayumi to suck the life out of so to speak.
After all, every time Ayumi feasted on a star's power, the star would age by a few million years. This could have drastic consequences to a civilization living within its vicinity, or more important the resources contained within the system.
As a result, Ayumi made sure to target stars that were either relatively new, and had billions of years' worth of life within them. Or stars so old they were going to go supernova sooner rather than later.