To reproduce:
- Set the AutoFileter property to true.
- Add filter descriptor;
- Start the application and type something in the control - you just need to filter the values so more than one entry is available in the drop down.
- Press Tab or click on other control.
- You will notice that the selected value is set, but the text is not synchronized.

Workaround:
void radMultiColumnComboBox1_Validated(object sender, EventArgs e)
{
    if (radMultiColumnComboBox1.SelectedValue != null)
    {
        string text = radMultiColumnComboBox1.EditorControl.CurrentRow.Cells[radMultiColumnComboBox1.DisplayMember].Value.ToString();
        if (text != radMultiColumnComboBox1.Text)
        {
            radMultiColumnComboBox1.Text = text;
        }
    }
}