I did not check into the exercise itself, but if your fingerboard hand is experiencing sharp pain, then just let up and come back to it later on. Your hands will toughen up in due time. Also, like others have said, make sure that your wrist is not all bent up because that can contribute to more strain.
Generally speaking, both hands should be hanging naturally without too much contortion going on. On the other hand, learning one-finger-per-fret position playing can feel like a contortion, but if you want to grow into an all-access player I strongly recommend it. When you know exactly what is under your fingers and can grab it without jumping around too much, it will help your time, your feel, and the quality of each note that you play. Later on when you are playing at a more experienced level, you will learn how to relax both hands and use less pressure for an effortless groove. This is a fantastic feeling when you start to discover it!
Now, as far as fanatically keeping your fingers down I would say the following: As a developing player, definitely work on that when you are practicing. This will help you become aware of just how much how your fingers need to move to get your groove out. Flailing your fingers about and exerting all sorts of extraneous energy can cause problems later on. I say can because just about every dogmatic maxim, especially about technique, can be subverted in one way or another, especially by a precocious and talented player. I mainly do keep my fingers down, but not always. For certain lines at the outer limits of one's technique I think that it can actually help your timing to "dive bomb" the note. Of course, at that point it is a highly conscious decision and not the result of exhaustion, or whatever. Watch cello players. They pick their fingers up quite high and come down on the note frequently.
So, there are always exceptions. But as you develop in the earlier stages work on keeping your fingers down and not squeezing the notes too hard. Your stamina and skill will increase with time.
Hope that helps.