WGS84 is a datum, not a coordinate system.
Are the data you projected in a GCS WGS84 coordinate system? That is, a Geographic Coordinate System, with units of decimal degrees?
or do you have a projected coordinate system with a WGS84 datum?
Or maybe a Web Mercator (projected coordinate system) with a WGS84 datum?
Is the data extent between -180 to 180 in the east west direction and 90 to -90 in the north south direction?
Just because a dataset has a coordinate system, doesn't mean it was defined properly.
Further, if the user defines one, because there was no coordinate system in the first place... they better define it correctly. That is the purpose of the last link.
If you don't check the extent yourself and confirm the metadata yourself, then "defining" a coordinate system can be an error prone venture. And, if it is defined wrong, projecting it won't make any better, but undoubtedly worse.