Adueñó comes from the verb adueñarse, meaning 'to take ownership of' or 'to seize'. It's a powerful and less common verb than simply 'to have' or 'to possess'.
In the song, Nicky Jam sings, "Que se adueñó de tu piel" (That he took ownership of your skin). This phrase conveys a strong, almost possessive, connection, implying a deep and intimate claim over the person's body and affection, making it a very evocative word in this context.
This song is pure drama! Nicky Jam is singing from the perspective of the 'other guy' in a love triangle, and he's tired of being a secret. He's telling the woman to come outside so they can talk, demanding she tell her boyfriend everything. He frames himself as the exciting, dangerous choice, the "bandido como yo" (a bandit like me) who she never expected to fall for.
He spends the whole song building his case, comparing himself to her current boyfriend. With her man, she's a "santa" (a saint), but with Nicky Jam, her inner "diabla" (she-devil) comes out. He's incredibly confident, telling her to let her boyfriend know that even when she's with him, "tú sabes que eres mía" (you know you're mine). He even calls the other guy a "sendo tonto" (a big fool) for not realizing what's going on. It's a bold and possessive anthem about a secret, passionate affair.