When converting from State Plane to Latitude/Longitude (WGS84), the underlying mathematical engine must handle both the grid projection and the datum shift.
The Two-Step Formula
First, the Easting/Northing grid coordinates are un-projected using complex polynomial formulas (like Lambert Conformal Conic or Transverse Mercator) to determine the geodetic latitude and longitude on the NAD83 ellipsoid. Second, a 3-parameter (or 14-parameter for higher accuracy) datum transformation is applied to shift that NAD83 coordinate onto the WGS84 ellipsoid.
Using un-audited converter tools can result in bypassing the datum shift, resulting in visually correct but mathematically disastrous 1m errors.