use strict;
use XML::Rules;

my $parser = XML::Rules->new(
    rules => {
        _default => 'content',
        'residue' => sub {
            my ($tag,$attr,$context,$parents) = @_;

            if ($context->[-1] eq 'residues' and $context->[-2] eq 'fe
+ature' and $parents->[-2]{feature_name} eq 'feature_one') {
                print "$attr->{residue_index} $attr->{residue_name}\n"
            }
        },
    }
);
$parser->parse(\*DATA);

__DATA__
<sas_residue_annotation xmlns="http://url/Schema" xmlns:xsi="http://ww
+w.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://url/Sche
+ma test.xsd">
...
[download]

or

use strict;
use XML::Rules;

my $parser = XML::Rules->new(
    rules => {
        _default => 'content',
        '^residues' => sub {
            my ($tag,$attr,$context,$parents) = @_;
            return ($context->[-1] eq 'feature' and $parents->[-1]{fea
+ture_name} eq 'feature_one');
        },
        'residue' => sub {
            my ($tag,$attr) = @_;
            print "$attr->{residue_index} $attr->{residue_name}\n"
        },
    }
);
$parser->parse(\*DATA);

__DATA__
<sas_residue_annotation xmlns="http://url/Schema" xmlns:xsi="http://ww
+w.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://url/Sche
+ma test.xsd">
...
[download]

The first version checks the parent and parent's parent tag name and the content of the <feature_name> tag whenever the <residue> tag is fully parsed, the second checks the <feature_name> whenever the opening tag <residues> is found and skips its contents if the <feature_name> is not the one you are looking for.