There are specific autoclaves like high pressure reactors that are equipped with stirring system. However, in the autoclave used in microbiology, the stirring phenomenon occured naturally due to the movement of the medium (liquid) during the boiling phenomenon inside the container (bottle, tube etc).
I agree with the explanation of Prof Alwazeer here. When the contents reach up to boiling inside a normal microbiological autoclave everything will be mixed well and finally, you will get a homogenized solution if you added soluble ingredients into your solution. The swirling which occurs inside the system during boiling will provide the necessary mixing or agitation. Otherwise, I suppose you have to look for an autoclave with an automatic agitation system.