This is one of those times when the precise "correct" phrasing is a bit debatable, but the initial sentence is not incorrect.
Conversationally, native speakers might insert words like you've suggested (for example, "there occurs a reduction" or "there is a reduction"). But in formal writing, we try to strip out superfluous words. So the author (or an editor) has done that here. But given that "occurs a reduction" is a bit stuffy-sounding even with the extra, more colloquial words in there, the edit to remove superfluous words has given us a sentence that almost sounds too formal.
We could rephrase the sentence many ways to make it still sound formal but not quite so weird. Just a few examples:
- During XYZ activity, A is reduced.
- During XYZ activity, (a) reduction in A occurs.
- During XYZ activity, (a) reduction occurs in A.
You'll see I included a comma after "activity" in each of these, which I think helps break things up. That works for each of these examples because what comes after the comma can stand as a sentence on its own in each case. (I.e., the part before the comma is a dependent clause, and the part after the comma is an independent clause.)
However, in the original sentence, "occurs a reduction in A" can't stand alone as a sentence, so we'd leave out the comma to clearly indicate that "occurs" is paired with "during XYZ activity."
Note, though, that the use of commas after introductory (dependent) clauses is at least somewhat a matter of style. Different style guides sometimes specify that an introductory clause does not necessarily need a comma after it, if the clause is short and the overall sentence makes sense without it. But my instinct is that omitting the comma in each of my examples would make the sentence hard to read.