JPEG Manipulation Quantization Double Dipping

When working with JPEG image properties (resolution, sampling, etc.) and you export the final product are you ALWAYS double dipping into 'jpegification'?

From my understanding when you load a JPEG image into an image manipulation tool (GIMP, Photoshop, ImageMagick, etc.) it goes like so:

1. Import JPEG


2. Decode JPEG into easier workable format (Bitmap)


3. Manipulate the pixels


4. Export back into JPEG (REDOING JPEG QUANTIZATION AGAIN, even if you copy the original JPEG parameters it's a double dip)

Am I correct in this?

Thanks!