To reproduce:

            this.radMultiColumnComboBox1.DataSource = this.customersBindingSource;
            this.radMultiColumnComboBox1.DisplayMember = "CustomerID";
            this.radMultiColumnComboBox1.AutoFilter = true;

            FilterDescriptor filter = new FilterDescriptor();
            filter.PropertyName = this.radMultiColumnComboBox1.DisplayMember;
            filter.Operator = FilterOperator.Contains;
            this.radMultiColumnComboBox1.EditorControl.MasterTemplate.FilterDescriptors.Add(filter);

1. Click the dropdown button, verify that all items list on drop down
2. Type into the textbox so only one item is left( e.g. "BERGS" )
3. While the drop-down is still opened, click the arrow button.
4. Focus another control on the form and then when the user clicks the arrow button, only one item is still shown in the drop down. 

Workaround:
        private void radMultiColumnComboBox1_DropDownClosed(object sender, RadPopupClosedEventArgs args)
        {
            this.radMultiColumnComboBox1.EditorControl.MasterTemplate.Refresh();
        }