Tabbing from table cell to table cell is the default behavior. If your document has legacy form fields and is protected for filling in forms the entry point in the document will be a form field and the tab will take the user to the next (created) field unless you use the procedures set forth in the link you were already given.

The key is to not have protection with exceptions, but to have legacy form fields in a document protected for forms.

In a document with content controls (rather than legacy form fields) the tab key does not move from field to field but may even (rich text) insert a tab within the content control.

Making Forms with Microsoft Word