On jest dokładnie tą osobą, którą chciałem zobaczyć.

English Translation

He is the very person I have wanted to see.

The provided explanation says that osoba appears in the instrumental case but the two modifiers are in accusative. Why would that be?

The explanation is not correct - all three words in question (, osobą, którą) are in the instrumental case.

It might be that the AI got confused, because ta (this) and która (which) have identical forms in both accusative and instrumental:

Jestem zainteresowany tą książką. / I am interested in [lit. by] this book.
Kupiłem tą* książkę. / I bought this book.

Którą kartę wybierasz? / Which card do you choose?
Którą kartą płacisz? / With which card are you paying?

*although officially not correct, this is very common in spoken language. The correct form is , so Kupiłem tę książkę.

As Hyacinthe pointed out, both forms use the same adjective form.
It makes sense if you split the sentence up. On jest tą osobą || you use instrumental case since it is the predicate nominative
then you’re left with [osobę] którą chciałem zobaczyć