thanks for your question.
TablePress does not use its own database tables, but stores tables in JSON format in a WordPress Custom Post Type. You will therefore find the tables in this format in the wp_posts table.
I strictly discourage you from accessing the data directly, as this is not supported by the plugin, and should not be done in WordPress anyway.
Also, for implementing the ColumnFilterWidgets, this is not necessary. You will only have to load that into the page, and adjust the call to the DataTables JS library.
As mentioned in the other thread about this, I'm planning to create a plugin extension for ColumnFilterWidgets, so if you are interested in this, I ask you for a few days of patience.