Was there any specific reason for which Austin had to approach Rhea?
Yeah, he had. Not because Rudolph asked him to, but rather, once Austin remembered the reason why Rhea seemed so upset because of that incident, he feared that the Protagonist might end up killing herself.
Although he didn't like the pinkhead much, it was an irrefutable fact that Rhea was a necessary asset for him and this world. She is the only living entity who can summon two soul shards at one time and can slay the Demon Lord.
As such Austin has to ensure that she doesn't end up taking any step that can change the world's fate for the worst.
That's why after talking with Valerie and asking her to remain nearby, Austin approached Rhea.
Valerie didn't seem to be willing but when Austin told her about Rhea's situation, she didn't say anything. She never stopped him from meeting her, however, when the reluctance in her eyes subdued, Austin felt comfortable approaching Rhea.
