How would time dilation by one character affect other characters in the same system?

I am in the midst of writing a book wherein one of my characters (Let's call her X) can affect spacetime, mostly by causing time to dilate.

My character is earthbound and a shadow organization discovers that she has these powers because she dilates time to recover from a personal tragedy. The issue becomes, how does the organization realize that she can dilate time in the first place? Would the characters on earth realize that time has been dilated or they will be oblivious to the same?

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How would time dilation by one character affect other characters in the same system?

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