"The state I live in (Washington) requires living there for 12 months in order to be a resident." I doubt that you will find any where in the statutes for WA that has this provision.
How long a person must have lived in WA to be considered a WA resident depends on the purpose.
For court purposes, for example, a person can file a petition for dissolution of marriage without children the day after the person moves to WA. All the person has to be to be a WA resident is to declare that the person intends WA to be the person's state of residence. For court proceedings involving children, because of the interstate compact, the children have to live in WA for at least 6 months if they come from some other place.
For in-state tuition purpose, a person has to lived in WA for at least 12 months without coming to WA primarily for schooling. This rule is the same in many states. So, a student coming to WA and going to school full-time will not become an in-state resident. Some students will go to less than half-time status for a year to become a state resident. The more the student acquires ties to WA (such as registering to vote in WA, getting a WA driver's license, buy a WA house, etc.), the more the student will be considered an in-state resident.
For traffic ticket purpose, the state allows a person moving to WA a grace period of 30 days to get a WA driver's license.