You don't need to actually follow/escort a group on their way to gather resources. I tried this several times and got nothing for it.
What seems to work for this is to go to a location that has a green icon for a resource (water, etc.) and just wait for
them to arrive. A group will eventually come up that is looking to gather the resource. Figure out who the "gatherer" is, and when they start to pick up the resource, you'll get the prompt (
on controller) to give some of yours to them (just make sure you have some of everything). Even if you come under fire, finish off the enemies and the gatherer should resume.
Once you initiate this, the achievement should pop.