The points I've chosen as examples above are not arbitrarily. They correspond with an influx of people that may be considered of other ethnicity, for example from another continent or culture. You describe the ambiguity of what you interpret as a border for "change of ethnicity" is precisely the problem with the term. Unless you create a consensus about the use in the specific discussion you may be misinterpreting what is being said.
The meaning of any natural language term is up to discussion some more then others.
Native is a lot more clear if used to refers to where a single person was born.
As a good example you yourself use "native" which is as messy, and complex as "ethnicity". You arbitrarily chosen Columbus arrival as definition point, which can make you feel comfortable in the moment, but it's neither universally accepted, nor universally applicable. Using the same logic it must be banished from serious discussion.