I have never thought of using this control from AcCustomize.dll. Seeing your question, I went for a try and did not have the issue of yours, well, at least for my very simplified code. Here is what I did:
1. Start an AutoCAD .NET add-in dll project.
2. Add necessary AutoCAD .NET references, including acCustomize.dll, which also be configured as "Copy Local" to False.
3. Add a Win Form.
4. Since the controls in AcCustomize.dll cannot be added into VS Designer's Toolbox, the MultiSelectTreeview control is added to the win form by code - adding it to form in the form's constructor and populating it in Form_Load event handler, as shown below:
public partial class Form1 : Form
{
private Autodesk.AutoCAD.Customization.MultiSelectTreeview _treeview = null;
private TreeNode _rootNode = null;
public Form1()
{
InitializeComponent();
_treeview = new Autodesk.AutoCAD.Customization.MultiSelectTreeview();
_treeview.Dock = DockStyle.Fill;
_treeview.CheckBoxes = true;
Controls.Add(_treeview);
}
private void PopulateTreeview()
{
_rootNode = new TreeNode("ROOT");
AddChildren(_rootNode, "First Level");
foreach (TreeNode node in _rootNode.Nodes)
{
AddChildren(node, "Second Level");
}
_treeview.Nodes.Add(_rootNode);
}
private void AddChildren(TreeNode node, string childName)
{
for (int i = 1; i <= 10; i++)
{
var text = childName + " " + i.ToString().PadLeft(2, '0');
var nd = node.Nodes.Add(text);
}
}
private void Form1_Load(object sender, EventArgs e)
{
PopulateTreeview();
}
}
5. show the form with MultiSelectTreeview with following command:
[CommandMethod("MyForm")]
public static void ShowFormWithTreeview()
{
using (var form = new Form1())
{
CadApp.ShowModalDialog(CadApp.MainWindow.Handle, form, false);
}
}
The modal form display the treeview correctly, which is no different from a regular Win form Treeview, except for each node having a default icon. I did not find a way to select multiple nodes, though (tried to hold either Ctrl, or Shift key while clicking nodes). See picture below:

So, not sure where the error you have is from. I used Acad2021, VS2019, and target to .NET framework 4.8. But I do not see other later versions of AutoCAD/.NET framework would make it different.