It's not a direct replacement for asynchronous, as reactive implies quite a different set of semantics. The collision is only in your misunderstanding of the pattern. The jargon is meaningful, not marketing.
Good to know. Then the "reactive" mentioned in the title is not exactly async, and not exactly as in "Reactive Extensions" either, so where can I find the intended meaning of "reactive" in that context?
Reactive is "things happen, I don't need to know, async".