To reproduce:

Add a row and a strip to the command bar, add items, set tooltips, make them hide in the overflow menu, they do not show their tooltips.

Workaround:

this.commandBar.Rows[0].Strips[0].OverflowButton.DropDownMenu.ToolTipTextNeeded += DropDownMenu_ToolTipTextNeeded;
this.commandBar.Rows[0].Strips[0].OverflowButton.DropDownMenu.MouseMove += DropDownMenu_MouseMove;

Point mousePosition = new Point();
void DropDownMenu_MouseMove(object sender, MouseEventArgs e)
{
    this.mousePosition = e.Location;
}

void DropDownMenu_ToolTipTextNeeded(object sender, ToolTipTextNeededEventArgs e)
{
    this.commandBar.Rows[0].Strips[0].OverflowButton.DropDownMenu.Owner = this;
    mousePosition.X += this.commandBar.Rows[0].Strips[0].Size.Width;
    mousePosition.Y += this.commandBar.Rows[0].Strips[0].Size.Height + 20;

    new ToolTip().Show("bbbb", this.commandBar, mousePosition, 1000);
}