A non-invasive plant stays put. It does not run underground into the lawn, it does not seed itself across a bed, and it does not turn up two properties over.
That matters more in this valley than the term suggests, because of how water moves here. Ditches and drainages run through and between properties, and they carry seed efficiently. A plant that spreads on its own on one property does not stay on that property — it ends up on a ditch bank, in a fence line, on open ground, and eventually it is somebody else's work to remove.
Colorado keeps a noxious weed list in three tiers, and some of what is on it was sold as an ornamental for decades. That is the pattern worth recognizing: the plants that become problems are usually the ones that performed beautifully, which is exactly why they got planted.
So anything that runs by rhizome or seeds heavily gets a second look before it goes on a plan, and a closer one near a ditch, a fence line or open ground. Most plants clear this easily. The ones that do not are worth catching at the design stage, when the cost is choosing something else rather than a removal contract.