Do they sometimes use the preterite and the present perfect tense interchangeably?

So, I’ve heard that these tenses are roughly the same as in English. I was watching a Mexican telenovela (because that’s my life now), and she said “Vine a decirle que deje en paz a mi novio.”

But obviously she HAS come to say that, she’s there right now. It reaches into the future, so shouldn’t she have said “he venido…” ? Or, just like in English, they sometimes just use whichever comes out first basically?