If Posted After Date

There are many ways of comparing dates. the following is perhaps the simplest (untested):

if ( in_category( 'photographer-interviews' ) && strtotime( get_the_date( 'c' ) ) > 1376524800 ) {
 get_template_part( 'content', 'interview' );
} else {
 get_template_part( 'content', 'blog' );
}

1376524800 is the Unix timestamp for 00:00 (GMT) on August 15 – that is, midnight of the 14th. So posts with a publication date of the 15th will return true.

If you literally only want posts after the 15th you’d use 1376611200.