The way I understand it is that tulips bloom in the spring, then the blooms die off. The leaves are soaking up sun and building the bulb up to store energy to bloom again. I think you can just keep them cool and dry until fall and plant them. Then next spring they'll start to get that "spring feeling" and come up where you planted them and they'll be happy and healthy. Many people plant tulips and then plant annuals on top after they bloom to cover up the yucky looking foliage of the tulips as they die back. I would do the same for daffodils, too.

The tulips you buy in the fall you then plant in the fall. They go through the natural process of the cold weather and then as the ground warms they "wake up". That's not very scientific. Some people put fall bulbs in the refrigerator and they imitate that cold spell and then bring them out so they bloom, but they have to be indoors because it's still too cold outside. It's called "forcing" the tulips. All that to say they need a time of being cold before they'll bloom again.

It is much easier to store hardy bulbs like daffs and tulips in the ground than it is to keep them viable for any length of time out of the ground. I would replant them in their new location ASAP. It really doesn't matter when you do this but it IS necessary to allow the existing foliage to yellow and dry and fall away naturally. That is what recharges the bulb for the following season.

You should also know that these spring blooming bulbs prefer to remain on the dry side during their summer dormancy so ideally best to plan them where they don't receive a lot of irrigation. And most hybrid tulips are not great about returning with the same vigor and flowering potential in subsequent years, in fact, many treat these more as annual bulbs and replant every fall with fresh bulbs. The Darwin hybrids are better at returning than most and species tulips are very good about returning and flowering year after year.