The problem is with local and lexical $_
Example:

use 5.010;

sub my_sub (&) {
    my $code = shift;
    local $_ = '1234';
    $code->();
}

my_sub { say };

given ("test") {
    when ("test") {
        my_sub { say };
    }
}
[download]

Output:

1234
test
[download]

Why?
Because my $_ (lexical - from the given/when blocks ($_ = 'test')) has a higher priority (aka is in the block where you are) than the local $_ (local - from the my_sub ($_ = '1234')

How to fix this?

use 5.010;

sub my_sub (&) {
    my $code = shift;
    local $_ = '1234';
    $code->();
}

my_sub { say };

sub my_sub2 {
    my_sub { say };
}

given ("test") {
    when ("test") {
        my_sub2();
    }
}
[download]