Hi Kristie! Many times while learning new exercises on a stability ball, the muscles which are all firing to maintain your balance will get fatigued in the process. This should eventually go away as you get acclimated to the ball.
The strain that you are mentioning could also be from lifting or turning your head to look at the screen while doing the exercise. You may not be doing this, but just in case, I thought I would mention it since this is the area that you would feel this tension if you were in a pike position with your head slightly rotated or lifted.
The first thing that you have to establish is an ease and confidence while using the ball. It is best to do this on your own time and at a slower pace than what we are doing in the workout. Once you feel that you have a connection with how to maneuver your body and maintain balance you will be much more confident using the ball in the workout(a little bit of wobbling is normal and will always be there).
The main form pointer that I can give you is to put all of your attention on your core. Tighten the core and use the contraction of the core to draw your buttocks upward. Many lose their focus because they are thinking of their wobbling legs and fearing that the ball will slide away in the middle of the upward motion (if thats the case then go back to working on building up your ball confidence a little longer).
I try to focus on my buttocks coming up rather than my legs rolling in. Tighten your core and imagine that you want to draw your tightened navel right up to the sky.
Hope this helps!
Whewieee! Thanks again for the tip!