You don't have to rinse off after having an Epsom Salt Bath however you will likely feel much better if you do rinse off in the shower to remove the Epsom Salt that may linger on your body.
I always rinse off after having an Epsom Salt Bath because if I do not I don't feel as clean and the Epsom Salt Tends to irritate my skin if I don't rinse off.
So I would recommend rinsing the Epsom Salt Off after soaking in an Epsom Salt Bath just so you feel better although you do not have too.
Whether you rinse off after the Epsom Salt Bath or not you'll still get the same health benefits of the Epsom Salt Bath and it detoxes your body.