Rightly pointed by Dan, it's an issue with the Coordinate System - Coordinate Values mismatch.
WGS_84_Web_Mercator (Auxiliary Sphere) is a Projected Coordinate System. Thus, its units are in Meters. When you add the values (in Decimal Degrees) using Web_Mercator, it considers the units to be in Meters, instead of Decimal Degrees.
Here is what you need to do (choose any one of the following).
1. While using Calculate Geometry for calculating Centroid, you can keep the default units, i.e., don't change the units to decimal degrees. Then the values will be correct when you add data in WGS_84_Web_Mercator (Auxiliary Sphere).
2. If you want the XY values in Decimal Degrees (Calculate Geometry), then choose the Spatial Reference as GCS_WGS_1984 while Adding XY Data (as pointed by Dan).
3. If you have ArcGIS Desktop Advanced License, you could use Feature To Point—Help | ArcGIS Desktop.
Think Location