It shouldn’t be because of your shoulder rest but if you are finding the new shoulder rest heavily tilts your instrument, you might be applying the shoulder rest on improperly. Feel free to take a picture of it and post it here for me to take a look.
There could also be another reason. When you are on the E string, your bow should be tilted at the angle to where it is close to the A string without touching it. If your bow is far away from hitting the A string while you are on the E, you could hit your leg while sitting down just because the angle of bow would be close to perpendicular to the ground. So to answer your question, try to get your bow closer to the A string while you are on the E. The only other thing it could be is that you could hit your leg if you’re sitting Indian style. I don’t recommend sitting that way; make sure you are sitting in a normal dining room table posture.