Personally, I make a splint with a stick when this happens and use rubber covered wire to attach the stick/splint above and below the breakage. This works well and in 3-4 weeks, often the splint can be removed to reveal a completely healed stem. Whatever you do, do not rub soil or spray the breakage with water, you need it to air dry and crust over. Even with the tape you used, there is a risk from excess moisture (sweating) under the tape, causing perfect conditions for fungus to grow and kill everything growing above the breakage. This is also why you do not smear dirt or spray water on the break, it just increases the risk of fungal attack.
There is no reason to stop your normal watering and/or feeding schedule, your plant will be fine, but I personally would remove the tape and make a splint out of a stick - a bamboo skewer works well, and remember, the break needs to air dry and crust over, just like a human wound. And just like a human wound, you don't spray that with water and keep it mushy soft, this just leads to infection.
Hope this helps, Organoman.