It says in both control scheme templates that holding right on the D-pad opens the emote menu, but it just accesses the quickslots like holding up does. Were there ever meant to be emotes in the PS4 version and if so, how are they accessed? Either way, it looks like something needs to be changed here.
Whoops. I thought I'd seen everything in the menus, but I guess I missed one! That'll teach me to go without sleep for a game, won't it? Thank you for answering my dumb question.