It says exercise like legislative control over all places purchased by consent of the legislature. What if the government didn't purchase the property but instead owned the land before the state was created? And what if as part of their enabling act the state gave up all claims to federal property within its borders? That land would still be the property of the federal government to do with as they wished.
Once a territory becomes a state, the federal government has no claims to the property except for use as ports or forts.
The property belongs to the state. I can't explain it as well as she does.