It probably is cycled, but only has enough bacteria to handle the percentage of the bio load for the tank it was running on.
Let's say, for ease of math, that your main filter is 4 times the size of the smaller filter, with 4 times the media. 20% of the cycled media is in the small filter, 80% is in the larger one. Look at your main tank, do you really think 20% of the stock are going to create 5ppm ammonia daily in anything larger than a gallon bucket?
By looking at your profile, no, unless your quar tank is one gallon. You might get 1ppm daily in a 10 gallon, if that. That is all the bacteria that has grown on the bio media of that filter. A recently cycled colony of bacteria will grow at a slower rate than that of a mature tank.
What to do? Only expect the media in the smaller filter to handle a corresponding bio load to the percentage of media it is in the cycled tank, which corresponds to the percentage of fish it can sustain. A production rate of 5ppm ammonia daily in any tank would be an unbelievably overstocked tank. Recently cycled tanks have a rather fragile colony of bacteria at first, the 5ppm used to do a fishless cycle is overkill, but provides a large bacteria colony, giving some measure of insurance.