What you’re describing sounds like your image is using a different map projection than Cesium expects. Cesium prefers the geographic projection (EPSG:4326), but some imagery providers can also use web Mercator (EPSG:3857). You can use tools like GDAL to reproject an image from one map projection to another.
You might be able to adjust corners by using a texture polygon, but it’s pretty unlikely this would give you good results, assuming I’m right that the problem is a difference of map projection. There’s a lot more to a projection change than adjusting corner points.