Presumes comes from the verb presumir, which means "to presume" or "to boast." It's an interesting word because it implies a certain level of arrogance or overconfidence.
In the song, the singer uses it to challenge his ex, saying, "Si me hubieras olvidado, así como lo presumes" (If you had forgotten me, as you presume/boast). He's suggesting that her claims of having moved on are just a facade, making the word quite impactful in conveying the song's central theme of lingering feelings.
Ulices Chaidez and Jovanny Cadena's "Si Me Hubieras Olvidado" is a sassy, post-breakup anthem where the singer confidently tells his ex that he's over her, even if she isn't. He points out that he moved on "sin la necesidad de que alguien más llegara a mi vida" [without the need for someone else to come into my life], while she, on the other hand, tried to heal her wounds with other people's kisses. He doesn't think it worked, saying, "Siento que no te salió, pues no te veo tan convencida" [I feel like it didn't work out for you, because I don't see you very convinced].
The singer's main argument is that if she had truly forgotten him, she wouldn't still be talking about him "con las nubes" [with the clouds]. He bluntly states, "De buena o mala manera, pero sigo en tu cabeza" [In a good or bad way, but I'm still in your head]. He even throws a bit of shade, mentioning that she didn't even mourn him, claiming he was "muerto" [dead] to her. It's a fun, slightly smug take on realizing your ex isn't as over you as they pretend to be!