Java fern doesn't have a cycle like that, in general it just grows bigger and bigger leaves over time. However, when conditions change a lot java fern often goes into a sort of panic mode where it produces lots of daughters as the leaves die or become damage due to the changed conditions. If you have new growth things should be fine, but expect to clip the leaves once they brown completely as they look like ass and never fall off naturally (java fern is tough even dead!).
Yes that's how it went for me too. When you buy Java Fern you usually get stray leaves. You;ll have to leave them in your tank for a few weeks/months for them to adapt to the water conditions and sprout new plantlets on their leaves. Once those have grown to about an inch of two, cut them off the main leaf (which should look pretty bad by now) and try and anchor them to a piece of driftwood or a rock. It's very easy to do but you have to be patient with java fern. It will not die but it will make you wait to see results.