If the media was mature, it seems as though you had some bacteria, just not enough for 3ppm's worth of ammonia (assuming that's what you dosed 6 days ago). What I think is happening is that you had some of both bacteria. The ammonia took 6 days to drop as there weren't enough of the ammonia eaters to get rid of all the ammonia straight away. They started by getting rid of a bit, and making a bit of nitrite; then as they multiplied they got rid of more and more, making an increasing amount of nitrite. The nitrite eaters may not have been present in any great numbers at the start but there were enough to cope with the small amount of nitrite made by the ammonia eaters. As the amount of nitrite increased, they too multiplied to keep up with the extra nitrite.
What is your nitrate doing, compared to your tapwater level? I know it's not a very accurate test but if it is going up it means you have nitrite being made and then turned into nitrate.
If your nitrate is going up, I would add another 3ppm dose tomorrow and measure both ammonia and nitrite every day.
If ammonia drops to zero but nitrite shows up, wait a couple of days and add 1ppm's worth ammonia and test again after 2 days. Continue like this until nitrite falls below 1ppm, then add a 3ppm dose and test after 24 hours. If both are then zero, your cycle will have finished.
If both are zero 24 hours after tomorrow's dose, add another 3ppm dose to check they are both zero the next day to confirm the cycle has finished.
Even having a few bacteria in the media can speed up a cycle enormously. It's getting them started that's the slow bit.