"Свой" is used when the possessor is the same as the subject of the sentence.
Yes. "Своих" would translate to "Your" to match "Ты".
Did it give you a different sentence?
Oh I thought "Своих" would be for plurals because их means their. Can you give me any resource where I could see the "Свой" form for each pronoun and cases?
All the forms are listed under "Declension". That should help some
It's not "his" parents but "your" here, the reflexive possessive «свой» and its variants always refer to the subject of the sentence as the possessor.
It's also not in the genitive, it's in the accusative; for animate nouns the accusative form always copies the genitive in the plural.