Possessives agree with the thing owned
In English, possessive words usually tell us something about the owner. If a man owns a car, we say it is his car, and if a woman owns it, we say it is her car. In Spanish, possessives work in the opposite direction. Words like nuestro and suyo change to match the thing that is owned, completely ignoring the gender of the owner.
This means a male owner can use a feminine possessive, and a female owner can use a masculine possessive. The only thing that matters is the noun being possessed.
The short words used before nouns, like mi, tu, and su, only change to match the number of the things owned. They do not change for gender. If one person owns multiple things, the possessive becomes plural.
Notice that in the second example, sus is plural because there are multiple cats, even though there is only one owner.
Other possessives, like nuestro, vuestro, and the longer forms like mío, tuyo, and suyo, must match the possessed noun in both gender and number.
This is where English speakers often trip up. When a man owns a house, the word for his is suya because the word for house is feminine. The possessive pronoun looks at the object, not the person holding the keys.
Because words like su and suyo can mean his, hers, its, yours, or theirs, they can sometimes be confusing. If you say a house is suya, you know the house is feminine, but you do not know who owns it.
When context is not enough, Spanish speakers clarify the owner by using de followed by the person. Phrases like de él or de ella identify the owner directly. Unlike possessive adjectives and pronouns, these phrases do not change to agree with the possessed object.
When choosing a Spanish possessive, look at the object being owned. The possessive word will always agree in number, and often in gender, with the noun it goes with or replaces, regardless of who the owner is.