Learn Finnish: Me valitsimme sinut yhdistyksen rahastonhoitajaksi. - We elected you as the association's treasurer.

This is driven by the verb valita (to elect, to choose). When you elect, appoint, or name someone to a position or role, Finnish uses the translative case (-ksi) for that position. It translates roughly to "as the treasurer" or "to be the treasurer".

Why is the object "you" expressed as sinut rather than the partitive sinua?

Because the act of electing someone is a completed action that achieves a final result, the object takes the total object form rather than the partitive. For personal pronouns like "you", the total object form uses the special accusative ending -t (sinut).

Does the word yhdistyksen (association's) need to agree with the translative case of rahastonhoitajaksi?

No, it stays in the genitive case. yhdistyksen simply tells us whose treasurer you became. A genitive noun modifying another noun never changes its case to match. However, if it were an adjective modifying the noun, it would have to agree (for example, uudeksi rahastonhoitajaksi for "as the new treasurer").

What are the building blocks of the compound word rahastonhoitajaksi?