A new conversation (or continued one) should trigger an alert like the other standard alerts when a new post is made to it.
The exception would be if the user has those alerts turned off.
Each user has to set that option... if you want to force it, it would most likely require extending the core XF functions via an add-on short of regularly directly editing the DB, which in itself is not a good idea.. not to mention that some users may not want that "feature" to happen.