It is not possible to have access to a private toilet tent while hiking. If you have hired one or it is included in your package, your private toilet tent will be available as soon as you arrive at camp, as your toilet porter will transport it between the different camps and set it up for you.
On longer hiking days that include a warm lunch stop, you may also have access to your toilet tent during lunch. If you need to use the toilet while you are hiking or between camps, your guide will help you find the best option.
It is almost always possible to find bushes or rocks en route that will allow you to go native in privacy.