I have added a word in the shared negative list, but I can see that the ad groups are still all green and 'on'. Why? Should I move all these ad groups to off status?

When you add a keyword in a shared negative list, Google stops triggering ads for these keywords. You can add these both in Adwords and AdNabu. Please note even if the ad groups are enabled, the ads wont be triggered. So we do not pause the search term ad groups in AdNabu specifically. Adding the negative keyword in the shared negative list is sufficient. You need worry about pausing the ad groups.