Usually this means "Don't try to trick me!"

"Dont pull that on me" is also a way of saying that you are not gullible and are not believing what someone is saying. You are not easily tricked. I hope that helps! 😊

"Don't pull that on me" could be a response to someone trying to get around a requirement or trying to get out of work, for example. If your employee said, "I have to leave work early to take my grandmother to her fingernail appointment" five days in a row, you could say, "Don't pull that on me." [There are better examples than this. Maybe someone else will write one.]