It's nothing to do with the verb - it's to do with the gender of the noun.
Bier - neuter noun
Käse - masculine noun
The possessive determiners (sein, ihr, mein, dein, euer, Ihr, unser) need endings like the indefinite article (ein, eine, etc.) does.
In those sentences, the verb is totally normal and needs the object to be in accusative case. The indefinite article in accusative case for a neuter noun is ein, so the possessive determiner needs to be sein. For masculine nouns it's einen so we need seinen.