Welcome to the bulbs forum, Joanna.
I dig hundred of tulips every year and store them over summer and all tulips I tried are perennial when handled this way. Essentially your doing as the bulb grower does in your own garden. The tricky part might be to keep the bulb size large so the bulb are able to bloom the following years, summer storage is easy. Some tulips can bloom from small bulb sizes and some tulips naturally forms rather large bulbs without dividing too much. These often perform the best in the garden. The worst case is a tulip that divides excessively while requiring a large bulb size to bloom
I read that in some areas in the US tulips (and other spring bulbs) might be harder to grow to blooming size because of high temperatures early in the year. Hopefully this is not true for you. This would essentially force the bulbs into premature dormancy which is something you don't want to as a long growing season gives bigger bulbs.
Fertilize every spring as they emerge to promote big bulbs. It is not usually necessary to repeat this.
Avoid shallow planting and possibly also excessively high storage temperatures in summer (the exception would be some species that require "summer baking" to flower the next year) as high temperatures promotes the growth of many small bulbs. Growing in pots also often makes the bulbs break down into many smaller bulbs.
The correct time to dig tulips for storage is when the foliage has died down and the skin of the bulb has matured. If the skin of the bulb is not fully mature it might be helpful to store the bulbs in dry sand as they would be more susceptible to drying out without their protective layer, but normally this isn't necessary.
Dry the bulb in room temperature or slightly above for a few weeks. Spread them out thinly in one single layer. Then store the bulbs dry in slightly bellow room temperature, still in just one single layer. If you plant late it might be beneficial to further lower the temperature some when autumn approaches. Too high temperatures, particularly when combined with long storage periods can give problems with deformed or aborted flowers, especially in sensitive cultivars. That said storage is usually not super critical as long as they are kept dry and well ventilated. Ventilation is needed as if some of the bulbs go bad, they will emit ethylene that hurts the bud inside the other healthy bulbs. Also avoid having anything nearby that emits ethylene, such as fruit or some vegetables. Keep an eye on them in the late fall as they might start to show signs of wanting to start to grow.
In some cases you might need to have a propagation bed where you grow the tulip bulbs to blooming size for the following year. I do this if I want more of a cultivar, but usually if a tulip has a tendency to break down into small bulbs every year, then I move on and try another cultivar instead with a better growth pattern for the home garden.
