I think you are suppose to leave the stems and leaves for a bit so they can store some energy for next year. I don't know the exact timeline, I usually leave them until they become more yellowish then will cut them all the way down.
Also, remember that not all 150 will come back next year no matter what you do. A bunch will just come up with just the leaves and no flowers, you will still get a decent amount that return, but they are not stable perennials that come back year after year after year. By the third year it will be even less.
Most of those public gardens where you see thousands of perfect tulips are planted every fall and dug up every spring after they bloom.