I plant mine immediately in the garden after they finish flowering because we don't have frozen ground. I find they bloom the next spring. There is no delay and they are not out of season so it must be something to do with different climates. However, the blooms are never as dense as the original indoor ones. They will come up every year thereafter. The paperwhites might bloom again if you lived in a frost free place where they grow outdoors in the normal course of things. All the hyacinths in this picture started life indoors in water.

The same thing happened to me. They were kept potted in the cold garage all winter, I was sure it was long enough. I "woke them up" in April, but the blooms were very low.

If you want to grow in soil, plant the bulb in soil right from the start. Growing in water is the whole idea of this method, hence the pretty vases. Water growing is not intended as a precursor to soil growing. After the bloom is over you can plant the bulb out in the garden.

Maybe we are confusing "chilling" with vernalization. With very few exceptions, spring blooming bulbs need a specified period of cool temperatures after planting to develop flower buds. This is called vernalization and is usually accomplished by just planting the bulbs in the ground in fall - the colder winter temperatures and soils combine to provide the necessary requirements. If you are forcing bulbs for early bloom, you must somehow replicate this natural process, typically by chilling the bulbs before planting.......some bulbs can actually be purchased pre-chilled or labeled "good for forcing". Chilling narcissus like Tete-a-tetes at 60F is not chilling them at all! They need temps at 35-45F for this process. The buds blasted because they did not receive sufficient vernalization. Some classifications of narcissus, like the jonquillas and tazettas (Divisions 7&8) originate from warmer climes and do not need similar periods of vernalization - these are the classifications that most often recommended for southern gardens or those in zone 8 and above. About 6 weeks before you want the bulbs to bloom, you need to bring the containers out of storage and into warm conditions and bright light, like a window sill. Keep the soil moist but not wet. Often forced bulbs will get tall, leggy foliage and flowering stems......this is an indication that they are not getting high enough light levels - not always an easy thing to accomplish indoors :-) Also forced bulbs do not last as long in flower as do their cousins growing outside, so don't be surprised if they only last a couple of days before fading.