The whole purpose of the nut being correctly is so the string can fit and move freely if need be... not out of the slot obviously... but this is why Graphtech nuts and such are possible, they are a "slicker" material, and why nut sauce is so popular, it prevents binding in the nut, so yes small movement is normal...
...however, if you are hearing what I call a "ping" sound from the movement, that means your string is binding... and it is holding its place despite needing to move, and then once enough force is placed on the string is finally shifts and makes a "ping" sound... make sure your nut is cut properly, I use Big Bends Nut Sauce, I absolutely swear by the stuff... it dramatically changed the tuning stability on ALL my personal guitars, and every guitar I setup for customers...