Perl: Using alarms with Post request produces odd behaviour - perl

Question

Initial Question
I am trying use Perl to make a POST to a remote server. I am using an alarm to set a hard timeout. When the alarm triggers, I am getting what I would consider to be strange behaviour.
This is the code:
eval {
local $SIG{ALRM} = sub {
die("Foobar");
};
alarm 25;
my $userAgent = new LWP::UserAgent( keep_alive => 1 );
$answer = $userAgent->post( ... );
# During a timeout, I expect that this code will not run. However,
# it does and it prints "Foobar".
$m = $answer->message();
print $m;
alarm 0;
};
alarm 0;
print "Done";
Put a sleep (or breakpoint) on server, so it will not respond and so that the alarm will trigger. When the alarm triggers, this will be printed:
Foobar
Done
My expectation was that this should print:
Done
Key questions:
Why is this happening? Am I using some kind of anti-pattern? Is using alarms, not a good idea, because underlying libraries may use them as well, and they may conflict?
What is the right way to solve this problem?
Appendix 1 - I know there is another method...
I know that I should be using:
$userAgent->timeout( ... );
And actually, I am. However, I would like to set a hard timeout as well, so that I can ensure that at most I will spend 25 seconds waiting on the request. Since the timeout associated with $userAgent->timeout( ... ); is reset each time the client gets something back from the server, it is not reliable enough.
Appendix 2 - Environment Info
#bolav mentioned that on his system, he could not reproduce the issue, I guess that it is possible that it is System dependant.
OS:
cat /etc/redhat-release
CentOS release 6.6 (Final)
Perl Version:
This is perl, v5.6.1 built for i686-linux
Appendix 3 - Answers on SO suggesting to use this method
https://stackoverflow.com/a/15900249/251589