If you have www.siteaddress.com as your primary domain then that means that your SSL certificate is applied to that domain/sub-subdomain combination.  Normally the non-www URL will forward to the www URL, but not if you explicitly add the https before it.  

So here's a break down.  What happens if you type the following into your address bar:

Just make sure you don't ever link to https://siteaddress.com.  Otherwise you should be okay, the only way someone would get that security warning is if they type in your domain, without the www, and WITH the https prefix.