You have been put on a program referred to as functional rehabilitation. This involves early range of motion to stimulate tendon healing and bracing to protect the healing tissue. This type of conservative care offers the best of both approaches.
Instead of putting the lower leg in a cast for six weeks, the brace is used. The cast would hold the ankle in a slight amount of plantar flexion (toes pointed down) with no movement allowed. The brace can be removed so you can actively plantar flex the ankle every day (usually from day 10 on). As mentioned, the idea is to use early range-of-motion to stimulate tendon healing without putting any stress on the tear.
Results of this approach have been very successful. The rerupture rate is the same between surgery and functional rehab. And of course, there are none of the potential associated risks that come with surgery (e.g., blood clots, nerve damage, skin infections).
However, on the plus side for surgery, patients go back to work sooner after surgery compared with functional rehab. All other factors (ankle motion, function, and calf size) are the same regardless of treatment.
If all other factors are equal, functional rehab is a good place to get started. If you are having symptoms of apprehension, it would be a good idea to ask your surgeon for a closer follow-up schedule. You can also request the opportunity to work for a short time under the supervision of a physical therapist until you feel comfortable with the program. With a little guidance, you will be able to tell the difference between acceptable and unacceptable ankle motion and tension on the tendon. The goal is to get a good result without rerupture and without the need for surgery.