Clause 4 in fact hooks to clause 2, despite the "sind". Without clauses 1 and 3, it would be:
Ihr Auftritt sind die[jenigen] zehn Minuten, an die sich der Zuschauer ... erinnern wird.
So, the problem ist that "Auftritt" is singular, but it's synomymous with "die zehn Minuten" (plural). This is grammatically correct, since, in cases of equalization [i'm not sure if equalization is the correct noun to translate "Gleichsetzung"...] of a singular noun and a plural noun, the verb adapts to the plural noun. Canoo.net has a nice example:
Mein größter Besitz sind meine Kinder.
Here, we have two nouns: "Besitz" (singular) and "Kinder" (plural): for the verb, you'll have to use the plural. "Mein größter Besitz ist meine Kinder" would be grammatically wrong.
The Duden gives a similar example:
Diese Sachen sind mein einziger Besitz.
Here, again, we have two nouns with different grammatical number; the verb has to use plural.
I think it's the same in English:
Those things are my sole property.
