To reproduce:
-add RadRibbonBar with RadDropDownButtonElement and use the following code:
 this.radDropDownButtonElement1.AutoToolTip = true;
 this.radDropDownButtonElement1.ToolTipText = "tooltip";

As a result, no tool tip has been shown.

Workaround:
public Form1()
{
    InitializeComponent();

    this.radRibbonBar1.ToolTipTextNeeded += radRibbonBar1_ToolTipTextNeeded;
    this.radDropDownButtonElement1.ToolTipText = "tooltip";
}


private void radRibbonBar1_ToolTipTextNeeded(object sender, Telerik.WinControls.ToolTipTextNeededEventArgs e)
{
    ActionButtonElement actionButton = sender as ActionButtonElement;
    RadArrowButtonElement arrowButton = sender as RadArrowButtonElement;

    if (actionButton != null)
    {
        e.ToolTipText = ((RadDropDownButtonElement)actionButton.Parent.Parent).ToolTipText;
    }
    else if (arrowButton!=null)
    {
        e.ToolTipText = ((RadDropDownButtonElement)arrowButton.Parent.Parent).ToolTipText;
    }
}