Normally the new tab page could only be set by an extension or by code in an Autoconfig file. I know how to work around an Autoconfig file on Windows, but not on Linux, so I will leave that to others to explain.

Back on the Add-ons: unfortunately, Firefox's legacy extensions have the capability of hiding themselves from the Extensions list on the Add-ons page. In order to be sure, you need to check in Firefox's Safe Mode.

You can restart Firefox in Safe Mode using either:

• "3-bar" menu button > "?" button > Restart with Add-ons Disabled
• Help menu > Restart with Add-ons Disabled

and OK the restart. A small dialog should appear. Click "Start in Safe Mode" (not Refresh).

Then check the Add-ons page. Either:

• Ctrl+Shift+a (Mac: Command+Shift+a)
• "3-bar" menu button (or Tools menu) > Add-ons
• type or paste about:addons in the address bar and press Enter/Return

In the left column of the Add-ons page, click Extensions. Then cast a critical eye over the list on the right side. Any extensions that Firefox installs on its own are hidden from this page, so everything listed here is your choice (and your responsibility) to manage. Anything suspicious?

To return to normal (unsafe?) operation, Quit Firefox and start it up again.

Just to be clear, does this problem affect only new tabs in an existing window, or does it affect any other pages? For example:

(1) Home page that appears in new windows when you use Ctrl+n or in the same tab when you press Alt+Home

(2) Startup page that appears in new windows when you use a desktop shortcut or other external method to launch a new window

Hi   !

Good for you to be on the alert, for search.rspark.com is a browser hijacker, which of course you need to get rid of.

As already suggested by jscher2000 :

Go to the 3-bar menu => Addons => and look for any unfamiliar or suspicious looking extensions, like e.g.:

SafeSearch Incognito SearchAssist Incognito

When you find any :   remove them.

But then :

Also look in :   Advanced => Network tab => Under : 'Offline Web Content and User Data'

Do the same in Windows' Control Panel => Programs.

However :   most malware will be 'hiding' somewhere , so let's run malware scans :

Further information can be found in this article :
https://support.mozilla.org/en-US/kb/troubleshoot-firefox-issues-caused-malware?cache=no

Run most or all of the listed malware scanners.
They all work differently   -   what one program doesn't pick up, the other might.

Also see : https://malwaretips.com/blogs/remove-search-rspark-com/