I see what you're saying. Either limb, when placed on the left side, seems to flex more than it did when it was facing to the right. That tells me that something in the way it's being held, and/or the shape of the handle itself, or the precise point the string is contacting the notch in the stick, is causing it. In other words, the tillering stick's mounting surface is uneven... i.e. not square... AND/OR the surface of the bottom of the riser piece isn't parallel with the back of the handle, or there is variation in the exact point the string is placed on the stick each time... or a combination of such things. These things should be made unconditionally true, double checked, and triple checked before tillering progresses. A few thousandths can project out to quite a noticeable difference in the length/leverage of a bow. There's not a better indicator of the accuracy and relevance, or not, of our tillering setups than what's being shown to you there. Seek the root causes, and adjust until each limb shows its mirror profile left and right.
These are additional reasons why I prefer the rope and pulley type tillering tree over the tillering sticks. I just find it easier to be consistent with them, and pull and hold truer to reality.
Not that it would make that big of a difference, but make certain your string is being held on the stick at the exact same spot each time. I did a quick check on your pics and it appears it could be off a little bit.