Review again.
That textbox setting had three places to change.
Those settings will keep it in the same place on the page regardless of the position of the text.

If you move the text where you inserted the textbox to a different page, the textbox will move with it, yes.

If you want it to appear only on a certain page, i.e. page 4, you need to put it inside an IF Field in a header or footer which appears on that page. The IF field must test for the page number.

You could use the construction found here: How to control the page numbering in a Word document
Your TextBox must be inserted inside the "truetext" of the IF field.