Catalyst::Plugin::RunAfterRequest behaves differently under server script and FastCGI - perl

Question

I'm trying to set up the Perl Catalyst plugin Catalyst:: Plugin:: RunAfterRequest and am seeing different behaviour when it is being run with the server script "APPNAME/script/APPNAME_server.pl" and the FastCGI process under Lighttpd.
That is, it works as expected with the server script, but when used in the FastCGI web server environment the request being returned seems to be blocked by the code allegedly running after the request is returned. This is easily reproducible with the code in Controller/Root.pm:
sub index : Private {
my ($self, $c) = #_;
$c->run_after_request(
sub {sleep 10;}
);
$c->response->body("foobar");
}
Running the test script returns a result instantaneously as expected, but will wait 10 seconds before a response in the web server environment.
Is there any configuration that needs to be made with Lighttpd or FastCGI to get this to work properly?
UPDATE:
As requested, sample lighttpd config:
include "common/mime.conf"
include "common/modules-core.conf"
server.bind = "127.0.0.1"
server.port = 6080
server.pid-file = "/path/to/lighttpd-6080.pid"
server.username = "user"
server.groupname = "group"
server.document-root = "/path/to/root"
server.errorlog = "/path/to/.errors-6080"
accesslog.filename = "/path/to/.access-6080"
include "common/index.conf"
server.modules += ( "mod_fastcgi")
server.stream-response-body = 2
$HTTP["url"] !~ "^/(?:img/|static/|css/|favicon.ico$)" {
fastcgi.server = (
"" => (
"appname" => (
"socket" => "/path/to/appname-fcgi.sock",
"check-local" => "disable",
"bin-path" => "/path/to/appname_fastcgi.pl",
"min-procs" => 2,
"max-procs" => 5,
"idle-timeout" => 20
)
)
)
}