I'm not a native speaker, but would agree that it sounds imprecise. To my understanding, that's a polynomial reduction of the time (O(n^2) to O(n): quadratic to linear) and not an exponential speed-up (O(2^n) to O(n): exponential to linear). 🤷 Colloquially, "exponentially" seems to be used synonymously to "tremendously" or similar.

They make the same mistake further down the article:

However, the implementation of the command suffered from poor scalability related to reference count, creating a performance bottleneck. As repositories accumulated more references, processing time increased exponentially.

This article writer really loves bullet point lists, too. 🤨

Seem ok to me, both in grammar and what it's saying about the change. O(N²) to O(N) would be an exponential drop (2 down to 1, in fact).

There isn't. This is the colloquial use of "exponentially" which is very obvious from the context.