Virus warning

Question

I just received a virus warning from a website www.thesafemac.com. It just popped up when I did a search on Google.  It also gave a phone number of 1-888-261-6418 to call.   I couldn't get out of that site either.  I had to close close out Safari.  I cleaned my History and Safari/Preferences/Privacy/Cookies.  I also ran updates.  Is this Apple warning me?
If this website is not Apple why are they warning me and not Apple?  If it is some non affiliated Apple outside source what gives here? 
How do I know that I have a virus, malware, trojan or whatever besides some outside source telling me there is something lodged in my computer?  My firewall is on and so the rest of the security settings.
In searching the community section for answers there is nothing whether to call Apple support in order to authenticate the warning and if they can eradicate the virus.  I bought Apple with security in mind.  How can an outside source (?) be warning me of a virus on my computer when I am not in www.thesafemac.com?
Now I am not sure to trust Apple. Yes, there are the possibilities. 
There is also no information on how much it is going to cost me for the virus or whatever search and eradication. My protection plan is expired and I was told by an Apple store that there is no such thing as extending or purchasing more warranty.
Thank you.
Mac Book Pro Early 2011 with Yosemite Version 10.10.2

Answer 1

These sites are scams. Ignore and move on. Do not click anything on the site or call any phone numbers. It is unlikely you have any problems on the computer.
In the event you have a problem exiting the page:
Helpful Links Regarding Malware Problems
If you are having an immediate problem with ads popping up see The Safe Mac » Adware Removal Guide and AdwareMedic.
Open Safari, select Preferences from the Safari menu. Click on Extensions icon in the toolbar. Disable all Extensions. If this stops your problem, then re-enable them one by one until the problem returns. Now remove that extension as it is causing the problem.
The following comes from user stevejobsfan0123. I have made minor changes to adapt to this presentation.
Fix Some Browser Pop-ups That Take Over Safari.
Common pop-ups include a message saying the government has seized your computer and you must pay to have it released (often called "Moneypak"), or a phony message saying that your computer has been infected, and you need to call a tech support number (sometimes claiming to be Apple) to get it resolved. First, understand that these pop-ups are not caused by a virus and your computer has not been affected. This "hijack" is limited to your web browser. Also understand that these messages are scams, so do not pay any money, call the listed number, or provide any personal information. This article will outline the solution to dismiss the pop-up.
Quit Safari
Usually, these pop-ups will not go away by either clicking "OK" or "Cancel." Furthermore, several menus in the menu bar may become disabled and show in gray, including the option to quit Safari. You will likely have to force quit Safari. To do this, press Command + option + esc, select Safari, and press Force Quit.
Relaunch Safari
If you relaunch Safari, the page will reopen. To prevent this from happening, hold down the 'Shift' key while opening Safari. This will prevent windows from the last time Safari was running from reopening.
This will not work in all cases. The shift key must be held at the right time, and in some cases, even if done correctly, the window reappears. In these circumstances, after force quitting Safari, turn off Wi-Fi or disconnect Ethernet, depending on how you connect to the Internet. Then relaunch Safari normally. It will try to reload the malicious webpage, but without a connection, it won't be able to. Navigate away from that page by entering a different URL, i.e. www.apple.com, and trying to load it. Now you can reconnect to the Internet, and the page you entered will appear rather than the malicious one.