Mail can't arrive in your Outlook Express inbox unless the program downloads it from Tiscali's server. So you must have Outlook Express configured to check for mail every time the program is started (and/or to periodically check to see if there's any new mail).
In Outlook Express, go to Tools>Options>General.
Click to remove the tick(s) alongside 'Send and receive messages at start up' and/or 'Check for new messages every __ minutes'.
Alternatively you can allow Outlook Express to continue downloading messages from Tiscali's server, but tell it to leave a copy of the message on their server. To do so, go to Tools>Accounts and click on the name of your account. Then click 'Properties' and select the 'Advanced' tab. Click to place a tick alongside 'Leave a copy of messages on server'. (You might also want to check one of the options below that one, so that messages will be automatically deleted after your chosen period). Then click 'Apply' and 'OK'.
Chris