It's basically a synonym for invited. Or from a dictionary: "asked or invited to do, provide, or contribute to something". Unsolicited is the opposite.

If you send someone an invite to a discussion, they're invited, whether you meant to or not. At least long enough to send a single reply (which may be multiple tweets).

Whether their response is a polite "you tagged the wrong person" or some awful screed does not change whether a solicitation happened. Especially because tagging someone is not a request for any specific sort of reply.

Relatedly, if someone is eavesdropping in public and steps into a conversation to make the most wonderful helpful and loved comment in the world, doing that was still unsolicited.