Possessive pronouns, like adjectives, change based on the gender and the number of the noun that they describe. мой - masculine, моя - feminine, моё - neuter, мои - plural (any gender). The gender of the noun is a complex matter, but as a rule of thumb, if the noun ends with о, its gender is neuter. (I can't think of an exception.)
Interesting! I didn't know торнадо is masculine. So are, apparently, евро and сирокко . Curiously, English wiktionary  marks торнадо as neuter, unlike Russian one.
You have to look at the final letter to find out what gender the word is in.
Words that end with а or я are feminine, о or е are neuter, ы or и are plural and everything else is masculine.
Words that end with ь may be both feminine and masculine!
There are a some exceptions though; кофе, папа, дядя, дедушка and мужчина are masculine.