get_theme_mod returning cached values regardless of apache restart

If the theme mod option has a value in database, your code is working just fine as it should return the value in database and ignore the second parameter. The second parameter is the default value to be used if there is no value is set. And the value is stored in database.

The problem is that you are wrong considering that the values of the theme mod are cached in database, they are stored in database, not cached; the query to get them from database can be cached but if you need to update the value of a theme mod, you have to update the value already stored in database. You can do it using set_theme_mod():

set_theme_mod( 'parallax_one_logos_content', 'new value' );