Does Unity modify mesh Normals or Vertex before rendering?

Or do I just have a bug in my own code?

I have a special mesh where my vertices are in groups of four. I would like to have a vertex shader that linearly scales so that with scale value of 1.0 all vertices would have orginal positions and with scale value of 0.0 all vertices would be in the center of their groups of four.

To solve this task I have calculated all centers and save offsets to them in Normals array. Then in shader I add them lineary multiplied with [0-1] scaling value.

Problem is that when I scale mesh with Material Property "_Scale" vertices scales toward the center as ment but also toward origo of the mesh. So the whole mesh scales down with _Scale property and it's not intended.

Mesh code:

 //tiles:
 for (int x = 0; x < currentTileCount; x++)
 {
     float newT = Mathf.Min(t / offsetOfAnimations.Evaluate(x / (float)currentTileCount), 1f);
     tiles[x].CopyVerticesToArray(newT, vertices, x * 4);
     tiles[x].CopyTrianglesToArray(4 + x * 4, triangles, x * 6);
     tiles[x].CopyColorsToArray(newT, vertexColors, x * 4);
 }
 
 //centers as normals
 for(int x = 0; x < currentTileCount * 4; x += 4)
 {
     Vector3 normalAsCenter = (vertices[x + 0] + vertices[x + 1] + vertices[x + 2] + vertices[x + 3]) * 0.25f;
     normals[x + 0] = normalAsCenter - vertices[x + 0];
     normals[x + 1] = normalAsCenter - vertices[x + 1];
     normals[x + 2] = normalAsCenter - vertices[x + 2];
     normals[x + 3] = normalAsCenter - vertices[x + 3];
 }
             
 mesh.Clear();
 mesh.vertices = vertices;
 mesh.colors32 = vertexColors;
 mesh.triangles = triangles;
 mesh.RecalculateNormals();
 mesh.normals = normals;

Shader code: (Problem is in vert function)

 Shader "NeduTileTales/OpaqueVertexColor" 
 {
     Properties{
         _Scale("Scale", Range(0.0,1.0)) = 1.0
     }
 
     SubShader
     {
         Tags{ "RenderType" = "Opaque"}
 
         Pass
         {
             CGPROGRAM
 #pragma vertex vert
 #pragma fragment frag
             //#include "UnityCG.cginc"
 
             uniform float _Scale;
 
             struct v2f {
                 float4 pos : SV_POSITION;
                 fixed4 color : COLOR;
             };
 
             struct appdata {
                 float4 vertex : POSITION;
                 float4 color : COLOR;
                 float4 normal : NORMAL;
             };
 
             v2f vert(appdata v)
             {
                 v2f o;
                 //pos calculations doesn't work as wanted
                 float4 pos = (v.vertex + v.normal * (1 - _Scale));
                 o.pos = mul(UNITY_MATRIX_MVP, pos);
 
                 o.color = v.color;
                 return o;
             }
 
             fixed4 frag(v2f i) : SV_Target
             { 
                 return i.color; 
             }
 
             ENDCG
         }
 
     }
 }