Cayena was madly in love with Raphael and the emperor is suprised to see that she understands how her duty as a princess comes before her love for Raphael. She also wasn't someone who'd willingly visit the emperor even on a bad day and she's even less likely to treat him so lovingly. (the eyes, her hands, gestures all show that) This 'new' Cayena is different and he wants to test her.
The king also finds it surprising that she knows Rezef is the one who poisoned her yet still wants to defend him. He likely wants to know her intentions and where she stands.
Also, Raphael looking pretty fine there lol