Finnish declension

Finnish does not have passive in exactly tha same sense as in English. Quote from Wikipedia article Finnish language: "The passive voice (sometimes called impersonal or indefinite) resembles a "fourth person" similar to, e.g., English "people say/do/". Your example "They were welcomed" is "Heidät toivotettiin tervetulleeksi", i.e. it really has an object, grammatically speaking.

Which form of the pronouns is used with the passive? Is it the nominative or the t-form?

It's the t-form.

Ok, then I think it would count as an accusative.

I found a scientific paper that uses the same argument. It calls it the "pronoun test": a form is really an accusative, if it turns into the t-accusative when you replace a word with a pronoun.