ArcGIS does not provide a piece of functionality that will let you do this directly out-of-the-box. In other words, there is no standard way for software to check what area a new feature is being created in and then populate a certain field in a feature class with a respective value obtained by performing a spatial join.
Alternative that can get you closer:
- Use feature templates for different states with predefined attributes.
- Develop a custom add-in (ArcObjects) which will have this logic (large work).
- Develop a custom Python add-in with some geoprocessing logic which will let you do this in several steps combined into one transaction (as appears to user). I'd go for this.
Of course if you don't need to get a point state attribute updated immediately after clicking a map when creating a point feature, you can wait after you are done with adding all points and then run manually a GP tool Spatial join which will let you transfer the state attribute to the point feature class depending on which state a point is located.