Using mature media, will speed up a cycle and you can fully skip the cycling process at some times. However this depends greatly on how much mature media you receive and the about of bacteria it contains. It can be somewhat confusing. I would not be surprised if the mature media does not fully cycle the tank when doing a fishless cycle. You will experience a mini cycle of sorts levels may be weird for a few days and you may get a low ammonia spike and nitrite spike during a short period of time.
When trying to figure how far some mature media will get you, you need to look at the bioload of the tank. For an example we will say its 15 mollies. Next you need to consider the amount of media the tank has. For simplicity we will say there are 3 sponges in the filter. Bacteria is spread evenly in the filter and you can take 1/3 of a tanks media without harming its cycle. So you get one of the mature sponges, its safe to assume this sponge will be able to fully support 5 mollies or a similar bioload without mini cycling.
If you add it to a ten gallon tank it will cycle it. As the bioload of 5 mollies is more than a 10 gal usually holds even if you are doing a fishless cycle. If you add it to a 55gal it will not do the same. The 55gal could support 5 mollies or a similar bioload right away with the mature media and you can slowly increase it until the tank is fully stocked. The fishless cycle though will allow you to fully stock the tank once it is finished. If you try this with the mature media you will still experience a cycle.
Of course this is normally more confusing as tanks usually have many different kinds of fish and often you are stocking different fish and trying to estimate there bioloads compared to each other.
Its confusing, but at least thats how I figure it out and cycle my tanks. I've never actually done a successful fishless cycle
. I've had no problems setting up a brand new tank, putting rummy nosed tetras or GBR in it a few hours later, then adding some mature media from another tank an hour later.
With your media I would add enough ammonia to the tank to read 4ppm if this is gone within 9hrs(I think) and you have no nitrites, but you do have nitrates. Then I would consider it fully cycled. You may see no nitrite spike as the bacteria are already there. You only see a nitrite spike when you don't have enough bacteria. The food(nitrite) builds up because they can't eat it all. If it doesn't build up it means there are enough bacteria to eat all of it.