Correlate is now commonly used as a verb. You pointed to the use of this word as transitive vs. intransitive, and stated that the latter is right and the former is, perhaps, wrong.
Note, unlike you, I'm not framing this as the difference between active and passive forms, because that distinction is just a red herring in this case. Consider this, the form that you find more comfortable to use is "A is correlated to B" is passive. However, it's not the fact that it's passive that makes it more natural to you. It's that it's intransitive, as in active form "A correlates to B," as opposed to its transitive form "we correlate A to B," that makes it sound right to you.
I must agree that the intransitive form sounds more natural, both in passive and active forms. Moreover, when Galton first introduced the term, he used it only as an intransitive verb, in passive form, e.g. "the length of the arm is said to be correlated with that of the leg." According to Pearson, it was Galton who first defined the term as a statistical concept in "Co-relations and their Measurement, chiefly from Anthropometric Data” in 1888. Although the word itself was used before in other contexts. Pearson's paper "Notes on the History of Correlation" is here.
Now, I have to break a bad news: both forms have been in use for quite some time. Here's an example from The Standard American Encyclopedia of Arts... published in 1898!
-- verb intransitive – correlate, correlating. To have reciprocal relation, to be
reciprocally relates, as father and son. -- verb transitive. To place in
reciprocal relation: to determine the relations between, as between
several objects or phenomena which bear a resemblance to one another
As you can see both intransitive and transitive forms are described, i.e. "A correlates to B" and "we correlate A to B" are both fine. See also this discussion.
The verb "correlate" was created by back-formation from the noun. For instance, apparently, a verb "translate" was created similarly from a noun "translation".
@kjetilbhalvorsen brought up an example "to google", but it's a different mechanism of word formation called verbing, and a special case of it too. Normally, verbing is making verbs from nouns like "medal" $to$ "to medal." In this case we take an eponym "Google" and make a verb "to google." It's similar to "Xerox" $\to$ "to xerox", and even an older example of a guy named Charles Boycott $\to$ "to boycott."
What's even more interesting about Google case, is that it's made from a recently made up word "googol."