Hello @Steve_Vick and welcome to Asana. You are referring to priority sections within My Tasks that is specifically structured to support the auto-promotion feature within Asana. There are some enhancements to My Tasks on the horizon that will likely support the ability to further automate what section a task is assigned when created or changed. Learn more about this here: Upcoming changes coming to My Tasks in Asana and the API! [breaking changes]
In addition to this, you do have the ability to sort My Tasks by Due Date, if you find that helpful.