Yes, area effects will cross through the walls
There is no language in any of the layers, or the general wall itself, that state it acts as cover or that spell effects can't pass through it.
Prismatic Wall is described as(emphasis mine):
A shimmering, multicolored plane of light forms a vertical opaque wall--up to 90 feet long, 30 feet high, and 1 inch thick--centered on a point you can see within range.
The wall itself is only light, with each layer providing a specific effect. An area of effect spell, such as fireball is not physically obstructed from passing through, so it can pass through.
Casting Through vs Effects passing through
The only relevant wall type is violet, which states:
While this layer is in place, spells can't be cast through the wall.
The limitation here is being able to cast through the wall. In this case, the spell isn't being cast through it. If the point of origin is outside the wall, then you are not casting through the wall. Your point of origin is outside, so you can cast. The spell effects can pass through because there is no limitation on that, only casting through it. The language from globe of invulnerability covers this specific case - and because the violet wall doesn't have that language, then creatures behind the wall can still be affected by a spell that is cast on the other side.
The creatures under the effects of the spell just happened to be within range of your point of origin. If your point, and therefore your spellcasting, doesn't cross the violet wall, then targets within range of that point but on the other side of the wall would still be effected.
A spell is only being cast through if the spellcasting portion of it crosses. For Area of Effect spells, like fireball, that is not happening. The effects of the spell cross over, but the spell is not being cast through the barrier.