You are correct in what you say. If you introduce proper controls, there will be less chance that an extraneous variable (EV) will become a confounding variable (CV).
In any experiment, there will be many extraneous variables. In the example from the csufresno.edu link below, you have such extraneous variables as room temperature, sex of subjects, and time of day. In the first experiment described in that link, the value of these EVs is the same for both groups. The value of the EVs did not vary when the independent variable (IV) varied. This prevents those EVs from becoming CVs because a CV must vary along with an IV.
In the second experiment described, we see EVs becoming CVs because they are not properly controlled. The groups each had a different IV as they should have, but the groups also had different room temperatures during the experiment and the experiment was conducted at different times of day. Because the experimenter did not control these EVs, they became CVs.
So, you will always have EVs. However, if you control for them properly, they will not become CVs as well.