Learn Finnish: Raitiovaunun tullessa matkustajien pitää etsiä istumapaikkoja. - When the tram comes, the passengers must look for seats.

This construction is a shorter way to say 'when something happens'. It uses the 2nd infinitive inessive form (tullessa) of the verb tulla (to come). The subject of this action is the tram, which must be put into the genitive case (raitiovaunun).

Could I say kun raitiovaunu tulee instead of raitiovaunun tullessa?

Yes, absolutely! Both phrases mean the exact same thing. The temporal construction is common in written Finnish to make sentences more compact, but in spoken language, you will hear the kun (when) structure much more often.

Why is the word for passengers (matkustajien) in the genitive case?

It is the subject of the necessity verb pitää (must / to have to). In Finnish, sentences expressing necessity require the person who 'must' do something to be in the genitive case.

Why is istumapaikkoja in the partitive case here?

It is the object of the verb etsiä (to look for). Because etsiä expresses an ongoing or incomplete action, it is a partitive verb and always requires a partitive object. This partitive rule overrides the usual rule where necessity verbs (like pitää) would otherwise take a nominative object.