Yes, some trophies auto-pop. Luckily, even some of the longer DLC-trophies. But mostly for exploration, levels & gear, kills and challenges upon doing "one more of them"
And if you transfer your character to PS4 and simply continue playing where you left off, you would earn the later story trophies first and would need a new playthrough to get the earlier ones.
I myself transferred my character from PS3 while playing my second Ultimate Vault Hunter Mode (so basically New Game ++).
So in the end, I was missing 5 story-related trophies. Went back to another save to get three of them. And finally started a new game overall to get the remaining two and the Plat
(And to your question: Yes, if you simply join other peoples games, you would earn the trophies out of order, too. It was the same on PS3 and also in Borderlands 1, if I remember correctly.