Why does my generated mesh have an offset?

Hello, everyone! I've encountered a problem when my mesh has an offset. I wanted to create a mesh around an object _objAround. But something went wrong.

First, I give the mesh coordinates via script _meshCoords. Second, I apply the same position to my mesh object as the object-around's one transform.position = _objAround.position. Third, I create new positions for the mesh this way: var meshNewPosition = transform.position + _meshCoords[i]. But as a result, it didn't work out.

There are three objects in the unity inspector: "Cubes" containing cubes representing the coordinates of the mesh, "Object Around" - an object I create mesh around and "Mesh" - an object containing the mesh and having the script.

Although the mesh box collider took the object-around position, the mesh still didn't (you can see it in the image). And also, I noticed that while the mesh pivot was at the object-around position, the center point was not (you can see it in the image as well).

Please, help me. Thanks in advance!

 using System.Collections.Generic;
 using UnityEngine;
 
 [RequireComponent(typeof(MeshFilter))]
 [RequireComponent(typeof(MeshRenderer))]
 
 public class MeshCreator : MonoBehaviour
 {
     [SerializeField] private Vector3[] _meshCoords;
     [SerializeField] private Transform[] _cubes;
     [SerializeField] private Transform _objAround;
 
     private Mesh _mesh;
 
     private void Start()
     {
         _mesh = new Mesh() { name = "Test mesh" };
         GetComponent<MeshFilter>().sharedMesh = _mesh;
 
         transform.position = _objAround.position;
     }
 
     private void Update()
     {
         GenerateMesh();
     }
 
     private void GenerateMesh()
     {
         _mesh.Clear();
 
         // Vertex Initialisation
         var vertices = new List<Vector3>();;
         for (int i = 0; i < _meshCoords.Length; i++)
         {
             var meshNewPosition = transform.position + _meshCoords[i];
             vertices.Add(meshNewPosition);
             _cubes[i].position = meshNewPosition;
         }
 
         // Triagnles Initialisation
         var triangles = new int[]
         {
             0, 1, 3,
             1, 2, 3,
         };
 
         _mesh.SetVertices(vertices);
         _mesh.SetTriangles(triangles, 0);
     }
 }

That's before any code working

Images: https://imgur.com/a/0MglSdV