Nevada Entity is Separate
Your Nevada/Wyoming corporation/LLC is a separate entity from your home state corporation. A corporation is an entity created by law, separate from you or any other corporation.
Whenever your home state corporation writes a check for valid business expenses to your Nevada/Wyoming corporation/LLC, you have created a tax deduction in your home state. The income has been transferred to tax-free Nevada/Wyoming.
Set up your special tax-free benefits, such as a medical reimbursement plan, retirement plan, etc., with the Nevada/Wyoming corporation/LLC (which will have no employees). This will enable you to take advantage of many legal ways to take money out of your corporation tax-free, without passing those same benefits on to other employees. (Some plans, such as a medical reimbursement plan, must be available to all employees.)