Cardinal tetras are also bigger fish when fully grown. Neons average 2.5cm/ 1" whereas cardinals average 3.5cm/ 1.5".
As the fish doesnt have any friends of its own species its behavior will be unpredictable. It might make the best of the situation and just join in with the neons. It might get aggessive and being the bigger fish it could turn into a bit of a bully. You should keep an eye on things or if the tank will accommodate some more fish why not increase the group of cardinals to 6 fish?