Many of the problems when using table styles relate to a lack of understanding of the hierarchy of styles and, since Word 2007, incorrectly setup documents.
MS made a crucial change for Word 2007 that implemented a tab in the Manage Styles dialog named "Set Defaults". By default, in a virgin template, the Normal style will match the settings in this tab. Unfortunately, many long-term users of Word were unaware of this change and continued their old habits of just modifying Normal. Newer users are mostly unaware of the existence of the defaults tab and remain blissfully ignorant of its importance.
If your table styles include text formatting it is critical that the table is inserted in a paragraph formatted with the document defaults. This means that there must be at least one style in your document/template that matches the document defaults, otherwise there is no possibility of the table style working correctly.
The Microsoft Word team explained this in two blog posts in 2008, little read at the time and now deleted, though, thanks to the Wayback Machine, they can still be found. The two articles are:
BEHIND THE CURTAIN: STYLES’ ORDER OF OPERATIONS and
BEHIND THE CURTAIN: STYLES, DOC DEFAULTS, STYLE SETS, AND THEMES