Actually, she had been standing in her current position for two hours. Kelvin hadn't noticed her then.
She took her time watching the soldiers of the Yggdrasil civilization. She was deciding who to make a move against when Kelvin came alone. Once she decided that he was troublesome, she decided to take him out.
However, Kelvin stopped what he was doing immediately she made that decision. Then he took off.
She doesn't believe that his action is a coincidence. Either he had noticed her or someone had tipped him off.
The first option meant he was dangerous, while the second option meant he was important enough to warrant powerful surveillance and protection. Regardless of which it is, she had to eliminate him.
So she took a step forward in his direction. This caused her baked figure to be exposed beyond the shadow of the tree.