In ArcGIS Online, when creating centroids for polygon features using the Find Centroids tool, the centroids are placed off-center or outside of polygon boundaries.
The Find Centroids tool is run on complex polygons with the true centroid option enabled. The centroids are created at an average position relative to the vertices in the shape, but not necessarily within it, as shown in the image above.
When using the Find Centroids tool, select the option contained by input features in the Show me output locations parameter, and run the analysis. This results in output centroid points located inside or contained by the bounds of the input feature.