Mature media has enough bacteria for that tank's bioload (fish mass plus food).
In order for it to handle a new tank it has to grow to handle that tank's bioload.
It can give him a headstart, but it won't instantly cycle it for him to just start adding fish.
As with any fishless cycling, he will need to add ammonia every day. He needs to test ammonia and nitrite daily. If he never gets any then yes, there was enough bacteria to instantly cycle that tank for that amount of ammonia and he can start adding fish slowly, as usual. If not he needs to keep adding it daily until the ammonia and nitrite both go back down to 0ppm. Then he can add fish.
It is possible to instantly cycle a tank for fish, but if the media you give him has so much bacteria to instantly cycle his tank, it took out that much bacteria from your tank. Using mature media to seed a tank is a good idea, but I wouldn't simply assume it will match his starting bioload. If he is too impatient to properly cycle the tank, maybe aquariums isn't the hobby for him.