Technically, you are not "granted licensure in both states." If you live in a compact state, check your license -- it should say something about the license having "compact privileges" (or something like that; I imagine the wording varies from state to state). This means that, as long as you maintain your permanent residence in your home state, your license will be automatically recognized in any
of the other compact states and you can work (with your one, original license) in any
of the compact states (but, technically, you're not licensed
in that state; they're just choosing to honor the license that you do
have. I realize that's a very fine hair to be splitting ...
The easy way to understand compact licenses is to think about your driver's license. The only way we are (legally) able to get in our cars and go on a road trip is because 'way back, many, many years ago, all fifty states got together and signed a compact
agreeing to recognize each other's drivers' licenses. Oherwise, each time you reached a state line, you'd have to stop and get a drivers' license for that state! However, as we all know, if you move
to another state, you have 30 days (or whatever the law is in that particular state) to get a driver's license in your new state of residence.
Same thing with the "compact license" in nursing. Your nursing license in your home state (if it's a compact state) allows you to work
in any other compact state because the states that have signed the nursing licensure compact
have agreed to recognize each others' licenses. However, if you move
to another state (including another compact state), your original license loses its compact privileges and you have to get a license in your new state (which, if the new state is a compact state, would again have "compact privileges").