Hmmm...this new information changes things a bit. If malwarebytes just found PUPs, then I have to assume what Norton found and removed was the trojan. So now we have a situation where you have had, in short order, both PUPs and genuine malware on your machine...and are concerned about reinfections....
As we've explained, malware (and PUPs), once quarantined, cannot be "sprung from prison," even by the uninstallation of the program that apprehended them. However...the most severe malware infections, like rootkits, are known for "inviting their friends to the party" once they've compromised a system. So what you've told us now leaves me with some concern that what you've got is this level of "über-nasty,” which has subverted your operating system enough to hide from any antivirus software, and the stuff that's been caught is just part of its symptoms.
This is not necessarily the case: at this point, it's equally plausible that Norton successfully blocked the trojan (as it appeared to), but not the PUPs (which, because they don't actually harm your system or steal your stuff, are outside its focus)...and then malwarebytes took out the PUPs, leaving you clean. But we now have to be vigilant a while longer, just in case.
So what I would suggest is that you redownload the free version only of malwarebytes (the paid version, including its free trial, contains real-time scanners that conflict dangerously with your Norton, but MBAM Free does not), from the link I provided above. Run a full scan, and see if it gives you a clean bill of health. If so, wait a few days (no more than a week), then run it again. Do not let it remove anything it might find; just copy-and-paste the log file it produces into a message here so we can see what we're dealing with. If your system is indeed clean, it won't find anything. If, on the other hand, there is a deeper infection, you will see PUPs and/or malware returning--not because anything "escaped" from quarantine, but rather because that's what that type of nasty does. If that happens, we will need to refer you to a "removalist" forum, where an expert with special training and tools can work with you one-on-one in a locked forum, to pull the thing out by its root(kit) LOL
Keep us posted, and we'll make sure you are, in fact, safe and secure!
V/R,
--DistEd2