Let’s approach it. Remember that directional prepositions can usually take either dative or accusative, depending on whether there is movement or not. In this case, the verb fallen is one that indicates movement strongly. So whenever you fall over, across or below something, it is usually taken as a movement and the case of the location is accusative.
Ich falle über den Rand.
Note, however, that it is also possible to have a dative here if the location is just the general place where something happened and not a location onto which you fell:
Ich falle unter der Brücke ins Wasser.
We now have a figurative meaning of the verb fallen — but luckily that doesn’t change the general discussion. Before we get to your actual case, let’s quickly discuss unter den Tisch fallen, an expression meaning more or less to get ignored:
Meine Anmerkung ist unter den Tisch gefallen.
Here again, the movement is in the direction of below the table. So you can think of something being thrown down there from outside the table.
Finally, arriving at unter etwas (ein Genre etc.) fallen, it is the same movement. Think of it as throwing something into a box on which the genre is written. But we’re not looking at a box, we’re looking at a label. We’re throwing something below a label. So it is only natural to signify movement by using accusative:
Tarja Turunen fällt unter das Opera- oder Symphonic-Metal-Genre.