While the relationship my partner and I have isn't really "secondary", I am the newest partner and she does have two other primary partners.
It definitely makes me unhappy if something is not going well on one of her other relationships and it makes me very happy when her other relationships are going well. This is because...well, I love her and want very much for her to be happy and I like the other two partners, so I wouldn't want them to be in a bad spot either.
While I don't consider myself responsible for her other relationships (and she doesn't consider me responsible for them either), I am quite happy to offer whatever support I can for her and them if it's needed. If that means stepping back for a bit, I'll happily do that. But those sorts of things are not up to me, just as what happens between myself and her is not up to her other partners. We all take responsibility for our own relationships and I trust that she will ask for what she needs and do the things she needs to nurture each of her relationships, including ours. And I also trust that her other partners have a similar mindset with regards to all of our relationships.