Unfortunately, it is very difficult to say what is wrong without debugging.
It looks like you are calculating the difference too early.
Try this way:

private bool waitUpdated = false;

OnlineMaps.instance.OnChangePosition += OnMapPan;

void OnMapPan()
{
    if (!waitUpdated) 
    {
        OnlineMaps.instance.OnMapUpdated += OnMapUpdated;
        waitUpdated = true;
    }
}

void OnMapUpdated()
{
    OnlineMaps.instance.OnMapUpdated -= OnMapUpdated;
    waitUpdated = false;

    // Prev OnMapPan content
}

If the problem persists, send me your project.
I will try to find the cause of the problem.

This is a video to show you what I mean (from second 10)
https://vr.alicefit.com/ice_video_20190808-192152.webm

I've seen that also just panning the map I get "OnElevationUpdated" at the end of the movement (that's why when I release the mouse the track get correctly calculated).
So I have idea that this 1st tip cannot be used... I'm doing it wrong?

This is my code (p.s. I'm still using Vectrosity but this is not the issue, because if moving the map I call "UpdateLine", just like with "OnChangeZoom" and with "OnElevationUpdated", it work.

private void Start()
    {
        OnlineMaps.instance.OnChangeZoom += UpdateLine;
        OnlineMaps.instance.OnChangePosition += OnMapPan;
        OnlineMapsElevationManagerBase.instance.OnElevationUpdated += UpdateLine;
    }

....

void OnMapPan()
    {
            ///Get the distance difference only for the 1st point
            Vector3 oldPos = _convertedWordlPositionsToList[0];
            Vector2 firstCoord = _coords[0];
            Vector3 newPos = GetWorldPositionFromCoordinates(firstCoord);
            Vector3 difference = newPos - oldPos;

            ///Apply the difference to all points
            for (int ii = 0; ii < _convertedWordlPositionsToList.Count; ii++)
            {
                _convertedWordlPositionsToList[ii] += difference;
            }

            ///Update line
            myLine.points3 = _convertedWordlPositionsToList;
            myLine.Draw3D();
        }
    }

void UpdateLine()
    {
        _convertedWordlPositionsToList = GetWorldPositionsFromCoordinates(_coords);
        myLine.points3 = _convertedWordlPositionsToList;
        myLine.Draw3D();
    }

It can also help:
- Track optimization (reducing the number of points).
- Caching values that are used in calculations.
- The use of overloaded methods, with a large number of parameters.

(Since I call GetWorldPositionsFromHorizon for each vertex in my track line when the map is panned or zoomed I'm worrying about performance issue)

I use this function to get XZ position, and next Y position from an array of longLat:

private Vector3[] GetWorldPositionsFromHorizon(Vector2[] _coords)
    {
        Vector3[] positions = new Vector3[_coords.Length];

        for (int ii = 0; ii < _coords.Length; ii++)
        {
            ///Get X-Z position
            Vector3 flatPosition = OnlineMapsTileSetControl.instance.GetWorldPosition
                (_coords[ii]);

            ///Get Y position (elevation)
            float elevation = GetElevationFromHorizon.instance.GetElevation(_coords[ii]);
            positions[ii] = new Vector3(flatPosition.x, elevation, flatPosition.z);
        }
        return positions;
    }

And your script just a little modified because I already have the longitude latitude of my point:

public float GetElevation(Vector2 longLat)
    {
        double lng = longLat.x;
        double lat = longLat.y;

        float elevation = 0;
        if (GetElevationFromTile(lng, lat, ref elevation)) return elevation;

        if (Horizon2_BingMaps.overviewElevation == null) return 0;

        double mx = lng, my = lat;
        OnlineMapsUtils.LatLongToMercat(ref mx, ref my);
        elevation = Horizon2_BingMaps.overviewElevation.GetElevation(mx, my);
        return elevation;
    }

As you can see in the attached picture in top view (orthographic) the shape created with my points is ok, so X and Z are right.
The elevation (Y) is wrong

2. Something like this:

using UnityEngine;

public class GetElevationFromHorizon : MonoBehaviour
{
    public Horizon2_BingMaps horizon;
    private OnlineMaps map;
    private OnlineMapsTileSetControl control;

    private void Start()
    {
        map = OnlineMaps.instance;
        control = OnlineMapsTileSetControl.instance;
    }

    private void Update()
    {
        Vector2 size = control.sizeInScene;
        float el = GetElevation(new Vector3(size.x / -2, 0, size.y / 2));
        Debug.Log(el);
    }

    private float GetElevation(Vector3 pos)
    {
        double lng, lat;
        control.GetCoordsByWorldPosition(out lng, out lat, pos);

        float elevation = 0;
        if (GetElevationFromTile(lng, lat, ref elevation)) return elevation;

        if (Horizon2_BingMaps.overviewElevation == null) return 0;

        double mx = lng, my = lat;
        OnlineMapsUtils.LatLongToMercat(ref mx, ref my);
        elevation = Horizon2_BingMaps.overviewElevation.GetElevation(mx, my);
        return elevation;
    }

    private bool GetElevationFromTile(double lng, double lat, ref float elevation)
    {
        double tx, ty;
        int zoom = map.zoom - horizon.zoomOffset;
        map.projection.CoordinatesToTile(lng, lat, zoom, out tx, out ty);
        OnlineMapsTile tile = OnlineMapsTile.GetTile(zoom, (int) tx, (int) ty);
        if (tile == null) return false;
        Horizon2_BingMaps.CData data = tile["cdata"] as Horizon2_BingMaps.CData;
        if (data == null) return false;
        if (!data.hasData) return false;
        elevation = data.GetElevation(tx, ty);
        return true;
    }
}

P.S. Make Horizon2_BingMaps.overviewElevation as internal.

1 - is there a way to tell the script at which distance from the camera the horizon should appear?
I try to explain better: in some situations the script create more horizon tiles on the back of the camera, and not in front.
As a result panning the Camera the orizon disappear, but as you move forward a little the new horizon tile appear (see pict in attachment).
I think that's some kind of optimization, so I'm wondering if it is possible to tell ("hey, I always want an horizon tile in front of the Camera... or something like that)

2 - Is it possible to get the elevation on the horizon tiles ? I have a very long path, and the piece of the path that is outside of the map does not get elevation

Many thanks!

Something like that.