Table styles are very particular when it comes to applying a table style that already has styles applied to the content. You're probably running into a situation where manual styling is preventing the table style from being able to format the table. Try this:
Now apply the Table Style and it should apply all necessary formatting.
You may also want to show the import options when you are placing the table and choose remove formatting from text and tables to clear out any Word formatting that might be coming in during import. Word is notorious for applying added formatting to content during import.