If I add a search term to a Manual Campaign should I add it as a Negative keyword to the related Auto Campaign?

Yes! Once you move a search term to a manual campaign, we highly recommend that you create a negative keyword (NK) for it in the auto campaign.  PPC.tools supports a one-click instant NK creation for that, right from the Analytics page. 

Our rules engine also allows for the easy promotion of search terms to keywords from within PPC.tools.