To reproduce: 
           radTreeView1.CheckBoxes = true;
            radTreeView1.TriStateMode = true;
            radTreeView1.AutoCheckChildNodes = true;

            RadTreeNode root = radTreeView1.Nodes.Add("Home");
            root.Expanded = true;

            RadTreeNode node1 = new RadTreeNode("Minimal");
            node1.CheckState = Telerik.WinControls.Enumerations.ToggleState.On;

            root.Nodes.Add(node1);

Workaround: first add the node to the Nodes collection and only then set its CheckState