As the key is not in the lock when it is locked via Nuki, you cannot push the inner key. It would also be stupid because Nuki would then no longer be able to turn the inner key. I hope I have understood you correctly 🧐😉

We have had a Kaba Star cylinder with a priority function installed specifically TO MAKE IT WORK. The idea of the priority function is precisely that you can unlock the lock even if a key is already inserted on the inside. To install the Nuki, we inserted a key on the inside and "slipped" the Nuki over it, and it worked without any problems. It is best to try it out if a key is inserted from the inside and this is turned a little, whether you can then unlock the lock from the outside with a key -> you may have to push the key in "relatively hard" so that you can turn it.