I treat my partners children as if they are my own and my partner can do the same. We have seven kids all together and run a tight ship. We talk about what we want for the children and how to meet everyone's needs.
All you can do is talk with your partners about what they want from you when you watch their kids. Are you a partner in parenting or just a babysitter? Kids can put a lot of strain on relationships. It's important to communicate.