Plugin encodes image source including @

Yes, that’s the problem with regular expressions, but you can double check all found strings and only have the “real” email addresses encoded:

add_filter( 'eae_method', function() {
	return 'custom_eae_encode_method';
} );

function custom_eae_encode_method( $string ) {

	if ( preg_match( '/^[_a-z0-9-]+(\.[_a-z0-9-]+)*@[a-z0-9-]+(\.[a-z0-9-]+)*(\.[a-z]{2,3})$/', $string ) ) {
		return eae_encode_str( $string );
	}

	return $string;

}