Hi David,
There are several methods to do that, but if I understand correctly, you want the pixels to contain nothing if not the object in question. The problem here is that the alpha information is needed to Composite things and, of course, for any color grading to match the other background.
The problem with "transparency" baked into pixels is that the transparency values influence the change you do to the non-transparent. For example, border pixes have 50% visibility. The whole image needs to be a stop darker, but the 50% transparency gets only a half-stop darker. The same happens to any blend mode applied or color correction/grading.
That is why the Alpha is preferably in a fourth channel for RGB and creates an RGBA image or two files, RGB and A.
If the transparency is in the mix already, it must be Un-premultiplied. Then, it is processed.
The ideal setup is Straight Alpha
https://help.maxon.net/c4d/2025/en-us/Default.htm#html/DRENDERSETTINGS-RDATA_GROUP_SAVE.html#RDATA_STRAIGHTALPHA
Here, the pixels are rendered fully as long as the transparency is not 100%, the slightest opaqueness, and the pixel is rendered fully for the object. Ideally. Now, any blend-mode or color change will be applied first, then the transparency (Alpha) will be applied) The merge node on the compositing software will then use the alpha value for both images to set the mount for each pixel in a mix, ideally to achieve 100%. It is not just slapped over a background.
Steve Wright's Book, Digital Compositing for Film and Video, is a great source— if possible, use the 5th edition. I'm biased here as I took a Class from him in 2005 about "Shake" compositing, and lately, I reviewed his last book. Read Chapter Seven, and you will know a lot about image composites.
In Ae, you can set the alpha version used for the file via "Interpret Footage"; if you have different files RGB plus A, then you can set this TrackMatte. If you don't work in float, set the Color Settings for the mask containing channel to Preserve RGB, as Alpha has no gamma.
I suggest using float-based formats, not integers (Gamma ≠1), and anything larger than sRGB/REC 709 as color space for good results. The processing "pipeline" should be larger if that is your output gamut. Different views about this exist, but we are no longer in the '90s. 
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Depending on the rendering engine, the options vary: Let me know if that helps or if you need something else about exploring this theme.
Enjoy your work.