I am confused. The pictures in this link https://imgur.com/a/rotDWTJ show the before AND after scan with the bottom picture being the after v-line??
If this is the case: In the bottom picture you can clearly see that volume is missing on the left side of the chin (compared to the other side), which in turn causes the slant.
Personally I don't think the lip lineup is the problem. Temporarily you could try to balance out the volume deficiency on the left chin side with filler.
I uploaded a pic for clarification: https://imgur.com/a/okIIoFO
Your observation of soft tissue having somewhat of a dip where there is a dip to the bone is a
CORRECT one.
What I can offer so far to this thread is what a 'V line' procedure is and what it really isn't. It looks to to me that the OP may have had somewhat of a V line to begin with and may have requested the chin to be made shorter. Although there are no bone scans of before any surgery, the 'before' presentation where you see the step offs flanking the chin, is consistent with the chin being made shorter (via a horizontal segment cut from the central chin). So, the 'V line' stated here that the OP ostensibly had was most likely a restoration of the chin that was prior shortened (setting it down lower). That's consistent with the step offs flanking the 'before' scan being blended in more with the after. (Refer to the illustrations to see what happens with different types of cuts.)
Since the presentation/communication from the OP is hard to follow, when that is the case, it is not uncommon for miscommunication to transpire during requests for changes.
I will also add that the OP didn't relay anything about a zygomatic osteo which is seen in the after and although I could not 'capture' the before soft tissue photos (presented later), I'm a loss to explain why the skin color was DARK in one of the soft tissue shots (could not 'capture' it on IMGUR) but very LIGHT in the close up of the chin.
Included here is an illustration, with some explanations of what I observed based on the illustrations and photos. That's all that can be offered given the OP's presentation.