The argument that the staff did not read Nicks mind completely ignores that the stick healed Monroe, knocked out armed police forces and brought Nick back to life after he was shot, without Nick's command.
This is my interpretation:
Nick did not instruct the staff. He had no clue what was going on, something clearly shown by Nick not believing his own eyes when he crashes true the mirror the second time. The only thing he did with the staff was killing Z. But he learned to use it in the 20 years that followed. The staff had divine powers and the killing of Z triggered a reset of the timeline. The vortex opened the portal and Nick came out on the other side. Different dimensions were, by the way, not completely unheard of in Grimm - Renard travels to another dimension to talk to Meisner. This was not a “normal” time travel, because the ring was removed from Adalinds finger, Z was dead, and the staff came true the mirror. Everything that happened in "the other place" did happened, but the bad things were reversed and only Nick and Diana knew the truth. It was the staff fulfilling Nicks wishes and following its new master.
This is my interpretation:
Nick did not instruct the staff. He had no clue what was going on, something clearly shown by Nick not believing his own eyes when he crashes true the mirror the second time. The only thing he did with the staff was killing Z. But he learned to use it in the 20 years that followed. The staff had divine powers and the killing of Z triggered a reset of the timeline. The vortex opened the portal and Nick came out on the other side. Different dimensions were, by the way, not completely unheard of in Grimm - Renard travels to another dimension to talk to Meisner. This was not a “normal” time travel, because the ring was removed from Adalinds finger, Z was dead, and the staff came true the mirror. Everything that happened in "the other place" did happened, but the bad things were reversed and only Nick and Diana knew the truth. It was the staff fulfilling Nicks wishes and following its new master.