Yes, after the fact; that is after my response they provided a definition.
> the person you're responding to shared the definition they are using
No, technically they didn't. They provided a definition, they didn't say it was the one they are using here. If it's not pedantic tangent, it seem correct to assume that is the definition they are using, but that's what "Implying" means, so I trying to explicitly get a clarification on that.
"Why?" you might ask? Not every discussion is in good faith. The more that is assumed, the more leeway you allow for people to weasel out of countered arguments.
Yes. They provided their definition in response to your (mis?)reading of their original words. They are not the party bringing bad faith to this conversation.