^Let's just think of it as a three-way relationship where they all love each other and Yui just happened to have the spot in the middle that night, then.
When they first met, they were cordial and Byakuren's subordinates were suspicious. In the present, after they've met many times, they're all lovey-dovey and Byakuren's subordinates are all "get a room".
Thought those two lovers were supposed to be 4 different persons here 'cuz ya see them looking kinda different with that flashy appaerance "nowadays"... O_o