Is it correct to say that import tariffs are unilaterally decided by the nation or bloc applying the tariff?
It depends on the importing country or bloc (X), and the country the import is coming from (Y), and the product category (Z).
If X is not a WTO member, and is not party to a trade agreement with Y, then tariffs can be set unilaterally.
If X is a WTO member (and has bound Z) or has signed a preferential trade agreement with Y that covers Z, then the tariff can be set unilaterally within (multilateral, bilateral or regionally agreed) limits.
If X is part of a free-trade agreement (or customs union) with Y that covers Z, then X is constrained to allow duty-free import.