You can do it in essentially the same way.
The trick is to get at the events--not of the ToolStripTextBox--but of the ToolStripTextBox.TextBox
You can do this programmatically
AddHandler ToolStripTextBox.TextBox.[EventName], AddressOf [NameOfYourEventHandlerSub]
Here's how you can show the list of available events from those pull-down menus at the top of the code window:
In your class, declare something like
Private WithEvents MenuTextBox as TextBox = Me.ToolStripTextBox1.Textbox
Now if you pull down the box on the left, you'll see MenuTextBox. Note that it is just a regular TextBox.
Select that, and on the right you'll see all of the events for the TextBox inside the ToolStripTextBox.
From there, you can do exactly the same thing as in that page to which you linked.