Actually it is just the opposite! See how the old bulb (with the roots and last year's dried bulb sheath) is above and the new bulb is below. The new bulb will not grow roots until fall time.
Tulips, like all plants, have a preferred depth to grow at. Even for the same species, this depth can vary depending on the type of soil and climate. For instance, a tulip growing in a sandy soil would likely want to be deeper than one in a clay soil. Most bulbs that need be deep in the soil to be happy, have developed ways to to alter their position in the soil to suit their needs. You have discovered one of the ways!
You are exactly right: the tulip plants growing in the pot were planted to shallowly, and the bulbs decided to
plant themselves deeper. Unlike some kinds of bulbs, tulips grow a new bulb every year, and exhaust the old one. If the bulbs were already at the correct depth, the tulips would have produced a new bulb at the same depth as the old bulb. But in your case, the plants decided to reach down and find a new deeper home for the new bulb to grow.
Your bulbs were, and probably still are, too small to produce a flower. Hybrid tulips are often hard to grow well enough to keep flowering, let alone grow them to flowering from a small bulb. This is because it is hard to duplicate they environmental needs outside of their native homes. Species tulips are much easier in this regard.
