Transition; feet are a little apart and skis are parallel.... That's all good.
...and here you're doing what you need to NOT do. You are moving your new outside foot waaaay out there, and brushing that ski's tail out to form the wedge. You are also doing this quickly. It's called a stem, and it's forbidden in the wedge christie. Do not move that new outside foot out and away, and do not turn that foot to brush the tail out to make a wedge; do not press hard on that outside ski by lengthening that leg.
Here's another transition. Looks pretty much the same as the first; you are fine in transition....
And here you are rotating your upper body, shoulders first, to point in the direction of your upcoming turn.
This is upper body rotation. It's another no-no. You are just beginning here to widen your stance as you
start to push that new outside foot out away from you, and as you start to brush its tail into a wedge.
Image below: You are now leaning in. You are also bracing (when your outside shoulder down to your outside foot lines up along a straight line), I presume to "pressure" that outside ski. So your wedge christie has a whole list of no-no's embedded in it:
upper body rotation
leaning in
bracing
a stem entry (stem christie)
varying stance width
These moves all work in some situations, and are all very common in intermediate skiers' parallel or nearly parallel turns. As an instructor you need to be aware of them and how they hinder a skier's progress. These movements might not be embedded in your personal skiing, but they are appearing in your wedge christies. But getting that wedge started for the wedge christie invites you, and any instructor seeking higher certification, to do them. You gotta get to a wedge from parallel somehow, right?
I wish we had a behind-the-skier-view of a passing wedge christie so I could show you how to get that wedge without pushing that foot out and brushing that tail away.
Here's a verbal description of what you need to do and not do:
1. Do not turn your upper body to look in the direction of the new turn in transition. Instead, work to keep your upper body facing sorta downhill the whole run, so that as your skis point left then right, your hips and shoulders will not be turning as much as your legs.
2. Keep your upper body upright, from the hips up; avoid leaning in.
3. Do not allow your outside shoulder-to-outside foot to line up along a straight line (bracing); do not press outward or downward on that outside ski to "pressure" it.
4. Do not do ANYTHING to the new outside ski or the new outside leg to make the wedge start. Erase that ski and that leg from your consciousness.
5. The critical and most difficult part is getting from parallel to wedge without brushing out that new outside tail. To make this seemingly impossible thing happen, you release your new inside ski by flattening it, you delay its turning, and the new outside ski should tip passively onto its new edge and start turning ahead of the inside ski. This is a subtle movement. It helps to have another instructor watching to let you know when you have it.
6. To make the examiners happy, try HARD to keep your wedge stance width the same as when you had parallel skis. This doesn't allow much of a wedge. Examiners will be watching for stance width variations. Keep your stance width stable. Remember, the wedge doesn't need to be wide. It should happen slowly, on its own, and feel "natural."
7. Once the tiny wedge happens and the turn starts, finish it as you do a regular wedge turn. Keep your upper body facing somewhat downhill and upright as the skis turn across the hill.
8. Bring the inside ski in to match the outside ski S-L-O-W-L-Y after the fall line. Your video shows you sliding it into parallel matching quickly. This shouldn't fail you, but it will lose you points (I think). Practice this slowness with diligence. Examiners want to see everything happening nice and smoothly.
By the way, I think this is all pretty pointless since we don't teach students to do a perfect wedge christie. But learning to do a wedge-christy by the book does show the examiners that you are willing to go through weeping and gnashing of teeth for their approval. They will reward you if you can do it.