The hidden Sith base isn't on Mustafar, of course. It's on Coruscant, and it's a simple apartment, holding only a few unremarkable people, and of course Palpatine, the innocuous Senator from Naboo.
At the time, Palpatine hasn't realized much that anything is wrong. He felt a small twinge when Maul died, but he didn't feel any specific details; as best as he can tell, the Queen should be arriving on Coruscant soon, with the Jedi eliminated, and it will be time to continue his plan. And so he's waiting, standing in the open area outside the Senate dome, ready to greet them when they land. It's only when they start to enter the orbit that he feels the presence of the Jedi - and of something else.
When the ship comes to a stop, Palpatine walks forward, tentatively, a smile on his face to mask his uneasiness. He sees the Queen, accompanied by a few handmaidens and soldiers, and some droids, and yes, there they are, the Jedi. Then they did defeat Maul. He's disappointed; he had thought Maul was strong enough to resist them, but -
Wait, who's that kid?
The kid with the Force swirling around her with more power than he's ever seen, a beacon that seems to reach out to him stronger than the Temple itself.
The kid with Maul's lightsaber hanging at her side.
There are many people who might be disturbed, to find their apprentice dead, to find their most powerful relic hanging from an eerily dangerous child, to find that their plans are going to have to change in the next few seconds. Palpatine, however, isn't feeling worried at all.
He's thinking, How can I use this?