They didn’t get Ebola, it’s the blood from people who have survived it that they are using for donations.
People get more contagious as they get sicker, so Duncan was less contagious while he was with them. Also, while he no doubt had very close contact with some of these people, it’s not like he was throwing up all over all of them all the time they were together.
And while it may be that his family, at least those ones who actually hail from Liberia might have some natural resistance or even immunity, I’m not even sure how or if that could be determined.
People who haven’t gotten “sick” still show up with the antibodies..and thus if they have the antibodies they are good candidates to donate blood if none is available from anywhere else.
If they have immunity, an antibody titer can be measured from their blood. Many people in Africa have anti-Ebola antibodies in their blood, indicating that they are probably immune.