I dont think its much of it being a reflection why she warned the duke if you read and remember how yvonne uses her power she always tells whomever she is manipulating to look at her so pen telling the duke to look in his cup when he is with her is for him not to get caught in her trance by avoiding eye contact.
contains spoiler!
The mirror of truth does the work to brainwash everyone (the fragment she have is the reason why she can manipulate them but since it shattered and incomplete, it is not fully working). Also telling them to look into her eye is a manipulation tactics to know whether the prey is listening to her or not like what happened to Eclise, since he wont listen to her there she tried to brainwash Eclise using his affection for Penelope. Penelope warned the Duke because she pity him, not for any other reason or brainwahing stuff. She warned the Duke to look at the tea cup to let him know that yvonne is not her daughter but a demonic being (layla) with no physical body from light, and following penelope advice he attack yvonne after knowing the truth that it is not her daughter anymore then yvonne shows her true color awakening the monster she plotted in the duke manor... i think this is the climax of the volume 4. poor duke she just want her real daughter.... ( T﹏T )
DAMN the moment Penelope realized that Yvonne reflection cannot be seen on the tea cup is a goosebumps T.T The artist did a great job!