Tuo: The person owns a masculine, singular thing (il tuo gatto)
Tuoi: The person owns masculine (or mixed) plural things (i tuoi gatti)
Tua: The person owns a feminine, singular thing (la tua cucina)
Tue: The person owns feminine, plural things (le tue cucine)
It's the same with all of the possessive adjectives/pronouns:
il mio/i miei/la mia/le mie
il tuo/i tuoi/la tua/le tue
il suo/i suoi/la sua/le sue
il nostro/i nostri/la nostra/le nostre
il vostro/i vostri/la vostra/le vostre
(except "loro" -- "loro" is always "loro". Just make sure the article agrees: il/i/la/le)
Each noun has its own grammatical gender and is completely unaffected by the grammatical gender of other nouns. It's only the adjectives that have to agree with the nouns they modify.
So it makes no difference if you're talking to a man or a woman, the noun "bacio" is masculine and so all of its adjectives, articles, and possessives must be masculine.