I noticed on Firefox with Firebug that your pages are all cached . Your session is working fine, but your page are cached, making login and logout quite (messed up).
Disable HTTP caching for your dynamic pages.
See Firebug output:
Response Headers
HTTP/1.1 304 Not Modified
Date: Thu, 14 Oct 2010 13:16:50 GMT
Server: Apache mod_fcgid/2.3.5 mod_auth_passthrough/2.1 mod_bwlimited/1.4 FrontPage/5.0.2.2635
Connection: Keep-Alive
Keep-Alive: timeout=5, max=100
Expires: Thu, 14 Oct 2010 16:16:50 GMT
Cache-Control: public, max-age=10800
Request Headers
GET / HTTP/1.1
Host: www.piataterenuri.info
User-Agent: Mozilla/5.0 (Windows; U; Windows NT 6.1; en-US; rv:1.9.2.10) Gecko/20100914 Firefox/3.6.10
Accept: text/html,application/xhtml+xml,application/xml;q=0.9,*/*;q=0.8
Accept-Language: en-us,en;q=0.5
Accept-Encoding: gzip,deflate
Accept-Charset: ISO-8859-1,utf-8;q=0.7,*;q=0.7
Keep-Alive: 115
Connection: keep-alive
Cookie: PHPSESSID=55aea3f792334052dc673f85feb0b54a
If-Modified-Since: Wed, 13 Oct 2010 13:47:53 GMT
Cache-Control: max-age=0
PHP manual has already an example on how to disable caching:
http://php.net/manual/en/function.header.php
<?php
header("Cache-Control: no-cache, must-revalidate");
header("Expires: Sat, 26 Jul 1997 05:00:00 GMT"); // Date in the past
?>