Never respond to such requests and only update or install Firefox via the official Mozilla servers.
There are lots of websites that try to seduce you to install malware and use methods like the one you got.

Thank you. So, how exactly do you find the appropriate updates for Mozilla or can it be set up to happen automatically?

You can update via the Help > About window or download and install the latest version from the Mozilla site.

You can find the full version of the latest Firefox 26.0 release in all languages and for all Operating Systems here:

• http://www.mozilla.org/en-US/firefox/all.html

how do i get rid of the pop-ups that keep suggesting this "update"?

How do I get rid of this pop up suggesting the update? I am running McAfee and Malwarebytes (the trial version).

Do you get this alert randomly or only when visiting specific websites?

Do a malware check with some malware scanning programs on the Windows computer.
Please scan with all programs because each program detects different malware.
All these programs have free versions.

Make sure that you update each program to get the latest version of their databases before doing a scan.

• Malwarebytes' Anti-Malware:
  http://www.malwarebytes.org/mbam.php
• AdwCleaner:
  http://www.bleepingcomputer.com/download/adwcleaner/
  http://www.softpedia.com/get/Antivirus/Removal-Tools/AdwCleaner.shtml
• SuperAntispyware:
  http://www.superantispyware.com/
• Microsoft Safety Scanner:
  http://www.microsoft.com/security/scanner/en-us/default.aspx
• Windows Defender: Home Page:
  http://www.microsoft.com/windows/products/winfamily/defender/default.mspx
• Spybot Search & Destroy:
  http://www.safer-networking.org/en/index.html
• Kasperky Free Security Scan:
  http://www.kaspersky.com/security-scan

You can also do a check for a rootkit infection with TDSSKiller.

• Anti-rootkit utility TDSSKiller:
  http://support.kaspersky.com/5350?el=88446

See also:

• "Spyware on Windows": http://kb.mozillazine.org/Popups_not_blocked