I found the above problem under the following procedure! It involves first merging two clips and then create a path with the the initial point almost identical to the current character position. When the play cursor moves CLOSE to the key frame of the path (the first frame where the path is picked, the character will just quickly shift for around 3 point (the position counter) and then slowly move back to the previous desired position. The following is the procedure and see whether someone can re-produce it and explain why? And best how to solve that!
Iclone 7-> new project; Apply Mason character (Double click Mason to make it go to the default position); Press G to show a top view!Browse Mason Motion->Perform-> Apply 'Walk_Bump_Object.iMtion'; At Frame 225, right click Mason-> Break and delete the 2nd clip; Now make sure the Reset Motion Root is checked (Under Animation, Motion Action Setting)At Frame 240, Browse CC_MixMoves_Male (Do not use G5_MixMove, it would mot work for G6 Mason) and apply Walk_Turn.iMotion (it is at the end of the list); Point to Frame 400 and break and delete the 2nd clipGo back Frame 1, and create a path with the start point very close to Mason's position at frame 400[Note: In iClone 7, the Actor's Modify->Attribute ->Transformation (Does not show the character's XZY numbers... I reported this a while ago or otherwise we can enter the co-ordinates for the path's start point)[Note that The path goes towards the left side (-X). At Frame 400, Mason faces the left hand side.]Now Mason picks the first point of the PATH. We will notice a tiny motion the character moves to the start point. NOW the problem is when we check Follow Path, Mason will turn towards the other side and we need to give it a -X direction Now moves the frame from 380 towards the end point, at around 390 or 39a, the character SUDDENLY moves towards the Y direction (Mason's right hand side) THEN SLOWLY MOVES BACH TO THE PATH'S START POSITION.See whether anyone can reproduce it! And help!This happens even before assigning a motion for Mason to move along the pathThanks

This might help picking the path more or less precisely. Though, there nothing precise when it comes to animating with the path.

It is a complicated operation and need time to digest; But the first thing I found is that in the very front part, you click Preview (Camera) & go to Modify and click an icon (cannot see clearly) and then the view has a scale shown. This icon is on the RHS of the Camera name. My Iclone 7 is missing that icon! I also did not find it in iClone6. Is it an add on?
Also did you notice that in IClone 7, when the character is moving in an animation, the Character's Modify-Attribute panel's tranformation XYZ did not change values. In fact these co-ordinates are very useful to allow the character to pick the path's initial point! Once the desired position to start the path motion, we can move the path's initial point to the exact co-ordinates. 

That is a ruler prop. Can be downloaded from here: https://forum.reallusion.com/442990/3D-Motion-Ruler-Boxes

As I said, there is nothing precise in iClone when it comes to motions. There is complex relationship between Avatar Transform Pivot and its Motion Root. They never match when avatar leaves world center.
Even if you have a Curve Editor, get the Motion Root XY and place your path at those coordinates, there would always be mismatch.
That is why I do what I do Match it visually in Orthogonal Camera top view with ruler prop. So briefly what is in the video again:

1. Match the Path Pivot to Avatar Pivot (you can actually do it after making a path by setting path pivot to the first point).
2. Slide down Path Constrain Blend (I do not know why it's there in the first place). Serves no purpose. (that was your main complain).
3. After Setting a Path Direction, there most likely would be a jerky move. Tweak Avatars' Pivot (usually with Z rotation). That would create a key in Path Offset.

4. (Not shown) Apply another motion to avatar and blend it with current Avatar pose. Another challenge...

If you are attaching the avatar to a path, and having the avatar follow the path, you need to use an "in place" motion, like a walk loop. Your avatar is trying to do two different things, I think. 

https://www.youtube.com/watch?v=DoogAD6H5xc&t=14s
I have made the above video my Reallusion Technical team. It details the operation I made. 
The operation includes loading Mason's standard move, CC's MixMotion and finally Mocap Spuny Move....
You could wind to the last 30 seconds of the video to see what happens with the character first dislocated away from the first point of the path BEFORE it went onto the path! And there were white dots connecting showing this movement path

For this problem, I finally got REALLUSION's technical support to solve it. I am producing a video to illustrate clearly how the problem happens and how it is solved by using the actor's constraint parameter's position marker! LOOK forward to that!

For this problem of actor (first receiving several different motion clips) dislocation when placed onto a motion path, IClone 7 Technical Support described a procedure to solve. Here is the video I made to describe it in greater detail
 
https://youtu.be/1dju9ntsQcUThere are also 3 others I made when I encountered actor dislocation when mixing motion clipsThe following are You tube links to 4 videos recording the actor dislocation problems I encountered when combining different motion clips as well as when the actor was assigned to a motion path.
Video One: IClone 7 actor dislocation with some motion clips having a different motion root or origin
       https://youtu.be/ELZJWudTPdIVideo Two: IClone 7 actor dislocation when 2 motion clips are being mixed https://youtu.be/C-0y5fcEZn8Video Three :  IClone 7 - Correcting actor orientation of a motion clip https://youtu.be/1DNSpywTWlAV

There is no need to post in more that one place.

Because your post is unreadable (black on dark-grey), I edited the text and embedded the videos here: https://forum.reallusion.com/FindPost480638.aspx.

---