Infinity stones are very capable of creating branched timelines.
The TVA has a desk draw filled with a host of infinity stones, presumably from pruned timelines where they were used for the wrong purpose. Timestones are very able to generate variant energy and create new timelines if used for the wrong purpose due to their immense power, like the other infinity stones. As such, the timestone being able to simulate these other timelines it could create is a pretty understandable power.
If he did create these timelines then he would be pruned, but he has the freedom of choice to create them. The infinity stone isn't necessarily able to predict well the actions of the TVA since their home is immune to its powers and so he might not see himself being pruned.
The Ancient One may well have some idea about the TVA.
The Loki writers hinted she did.
"We don't really know. It would be interesting if they did," Waldron told The Direct. "I think what we see with the TVA is, whereas the folks at Kamar-Taj are dealing things in a magical way, the TVA is paperwork. It's bureaucracy. It appears to be a little more science-based."
If she did know about them, her statement is accurate. Their branch may be pruned by the TVA, and millions would suffer.
She doesn't necessarily know the full picture. She sees things from a magic side of things, which may well carry hints, but not all of the picture. -- Doctor Strange.
The Ancient One: Each of those maps was drawn up by someone who could see in part, but not the whole.
Dr. Stephen Strange: I spent my last dollar getting here on a one-way ticket, and you’re talking to me about healing through belief?
The Ancient One: You’re a man who’s looking at the world through a keyhole, and you spent your whole life trying to widen that keyhole. To see more, know more. And now, on hearing that it can be widened in ways you can’t imagine, you reject the possibility?
In Doctor Strange in the Multiverse of Madness we may see how much they know about the TVA. What they do know will likely be mystical, not scientific.