I think the most natural way to reference the movie is:
Last night I watched a movie with a really interesting storyline.
However, if you refer to the storyline separately, in the case of a movie, it can be present or past:
Last night I watched a great movie. The storyline was/is very interesting.
The fact is that a work of literature or a film, or anything immortalized in any medium which is always accessible can be referred to in the present. However, it can also be referred to situationally in the past, in a past context.
Note that in American English, we see movies in a theater, and watch movies at home.