What happened is that the client installed the management console and the distribution service on that new server using a second publisher license.
For the rest of the services he pointed them to the first server (same values as in the console of first server).
He then added a new task for that dashboard in the second console (separated from the other list of tasks).
My understanding is that it is possible to force a task to run on a specified node. This by crearting a "dedicated task". That is, a task in a defined "Publisher Group" linked to a QDS node: