I think if you said
with the meaning "[in order] to talk to that person, I [will] go to a cafe."
then that could work.
But I'm not following
= "I to talk with that person and go to the cafe." ?
or "when I talk to the person, then I go to the cafe" ?
Or at least that's what と would do for me meaningwise.
If the と you're using is the one for conditionals, then it takes on a meaning of "when" as in when the condition preceded by と is met, then the second half follows.
= if/when I talk to that person, I receive permission to enter the cafe. (apparently it's a pretty exclusive joint!)
I think that's what the book is trying to tell you. Or rather と has a 前後関係 not matched by the other conditionals possible in Japanese such that the left precedes the right.
AとB means whenever in the sense of "Whenever A has occurred, then B always occurs after that" or "After A has happened, then B happens." Thus, it's the best way to translate "if, then" sentences in logic. It does not refer to concurrent events of A and B, because it temporally distinguishes the events.