The soldier came to the welcome center to locate Rhea, and given the fact he knows she's an integral part of bringing the newcomers here, it seems like a logical assumption that she would be in the area. He hasn't had much luck finding her, and while he hasn't let it get to him, he has been searching on and off.
That's why when he spots the hooded figure clearly trying to escape without being seen, he follows outside quietly.
excuse me white blur have you seen a priestess and/or cat
That's why when he spots the hooded figure clearly trying to escape without being seen, he follows outside quietly.