I figured out what causes this issue. In newer version of core-emails.php:
add_action( 'af/form/submission', array( $this, 'send_form_emails' ), 2, 2 );
has been changed to
add_action( 'af/form/submission', array( $this, 'send_form_emails' ), 15, 2 );
If I change priority back to 2 all works fine, but core will be overwritten with next update.