Yes, it is this "again" character!
This "again" indicates that you and Purple Obscurity have met before, and there seems to be some tacit understanding between you two.
Purple Obscurity is always cold when talking to people. Her tone with you and Huang Quan just now was almost the same, but as a possessive woman, Hua Jieyu sensed a potential crisis from Purple Obscurity's cold words.
She is a woman with strong possessiveness and absolutely does not allow her man to have a stunning presence like Purple Obscurity, for that would make her worry every day that your heart might completely belong to someone else. This isn't to say she lacks confidence in herself; it's merely precautionary.
In fact, this is also a manifestation of Hua Jieyu caring too much about you.