The odds of an instant cycle are pretty low but it's something that can happen. The goal is to get enough BB into your new tank from an established one to support your bioload.
So say, you don't see a spike in ammo or nitrite with the neons you may have one after you add something else because perhaps the swishing provided enough bb to handle the bioload of the neons. Again I doubt this as people can add old filter media and still go through a cycle, I've never heard of swishing alone cycling a tank.
Essentially you are doing a fish in cycle, even these safe start products are essentially doing fish in cycles. Sadly most people don't realize that they still need to keep on top of their parameters and od the needed water changes.. The swishing will probably help out of course. You will need to continue to test over the next several days and do water changes as needed and when you begin to add more fish remember there is that adjustment period of your BB to build itself up to handle the new bioload as well.
