I haven't ever used binding ease, but I just watched the video and I noticed a few of things she does not explicitly mention. 1) Her right hand (on the left side of the screen) is keeping the two edges very well aligned as she feeds the strip in. 2) The fold in the binding is as close to her body as the device will allow. 3) She's sometimes (often?) got tension on the strip from *both* her hands (so both hands are gripping a fixed point and moving sideways with the strip).
If you weren't doing some of those things, maybe adding them will help? Good luck!