Yep. In 90 seconds you certainly should be able to get across the emotion. Even if you don't get the exact story, it should be something where you can tell happy from despair and frustration from terror without the back story.

Even if no one ever says a story, the dancers will have a backstory to the dance (either given to them or one they made up) to help with evoking the emotion.

Now once you get props and lyrics in there that often give a big hint to the storyline of the dance and with more time for context and perhaps something like, I dunno, a set, the story may not need to be overtly stated.

Although stating what the story is can sometimes hurt as much as it helps. If you set up a certain expectation then you need to deliver on that. Like sometimes you get someone with a goofy grin on their face all the darn time and that can blow the mood of a piece if you know that isn't the right emotion.