I had a similar issue were I had already completed the 1st Poppi date, but still didn't have the arcade mode unlocked. Had to hit the unlock all button. I guess with all these new updates, I have a few other questions.
#1: Can you go on any other dates besides the first 3 with Sammy, Poppi and Nile?
#2: What's the purpose of the pinging in arcade mode as well as those little tokens that appear when you do?
#3: How do the mini games affect the playthrough?