I don't think you need to worry about negative associations. Children this young tend to live in the moment, Their quick to be upset but just as quick to forgive and forget. Your daughter has likely already forgotten about the staircase or being upset. I doubt she has made any negative associations that need to be broken.
In fact I would say trying to hard to break an association right now would only be drawing attention to the stairs, telling her she should be associating 'something' with them if mom makes a big deal about them.
Your right she probably did realize you were gone and was upset over it, that is normal and acceptable. Separation anxiety can be strong when a child is first weaned from their parent.
However, as I said kids live in the moment. As upset and distraught as a child can be when their parent first leaves, with care and loving attention from the staff they will cope with it, and then return to playing. With a good staff usually a child will be comforted and their crying will die down within 10-20 minutes even for first time separation, and afterwards the child will go back to having fun until their parent returns.
As someone who has done daycare quite a bit I'll say the honest truth is there isn't any great way to make this easier for your child. Honestly the best thing you can do is make sure their in good hands and then leave. Yes eventually the child will learn your gone and be upset for awhile, but they need to learn that it's okay. That nothing bad will happen while your done, and that eventually your come back. After a few days of this they tend to get the message and become better about seperation. After that they may cry right when you leave, though that's more in the hopes they can manipulate you into staying then real anxiety, but generally their go back to playing almost as soon as your gone.
As anyone who has done childcare will tell you though, it's best to leave for good. Trying to slowly ease them into separation, by doing small breaks and coming back or slipping away until they cry, doesn't really work. As you already said, the lesson the kids take away is often if they cry long enough their parent will come back, and even if they don't learn that the constant coming and going causes kids to pay more attention to the presence, or absence, of their parents. It can be hard, but it's best to leave for good and let them learn that things really will be okay without you, that they can even play and have fun while your gone.
There was one little girl, Autumn, that I still fondly remember years later with the worst apparent separation anxiety ever. She would ball her eyes out whenever her parents left, you would think she was dying. No one would guess that she actually loved being there with us, she was a real extrovert at heart and enjoyed her chance to be with other kids her age. I'd take her and shoo her parents away while she acted distraught, then the moment her parent's were out of site I'd do something to distract her for a second from her crying and the moment she stopped she would remember she was in a classroom full of toys and kids and go around having a great time. Her parents thought I was a miracle worker for getting her to switch from crying to playing so fast, but the truth is most kids just don't know how to handle the act of separation itself, as soon as it's over their ready to move on and start playing.