Ixtlanian,
1. The two scan options that Mithun suggested would not have shown up as a scan in the scan for threats section of the client. The fact that you deleted any scans in this area has no affect on these triggered scans running or not, they are options in the registry not displayed in the GUI and the best way to change these options is via policy.
2. It is impossible to give a 100% answer from a short forum post with no logs. But based on your second post with the screenshot it is most likely either a Defwatch quickscan or Defwatch wizard scan of the quarantine. On the client if you go to view logs-> virus and spyware protection->scan log on the right most column will display logged by, I am guessing this will say Defwatch Scan. The quick scan would be resolved by unchecking the run a active scan when new definitions arrive, as suggested by Mithun. The second of which would be resolved by going into your AV/AS policy on the SEPM then quarantine then change the option to "Do Nothing" under when new virus definitions arive.
For a unmanaged client in order to disable the Defwatch wizard scan you will have to make the following registry change below.
HKEY_LOCAL_MACHINE\SOFTWARE\Symantec\Symantec Endpoint Protection\AV\Quarantine\DefWatchMode=3 (REG_DWORD)
DefWatchMode
value action
0 Automatically repair and restore files in Quarantine silently
1 Repair the files in Quarantine silently without restoring
2 Prompt user
3 Do nothing
So in this case you would want to set this value to 3. Now these are instructions for a 32bit client, if you are dealing with 64bit its going to be under the Wow6432Node then symantec.
Now I may be incorrect but this is the best answer I can give you with the data provided.
If you want a more detailed analysis of this issue or you want a faster resolution for this issue or any future issues I highly recommend calling in and opening a support case.