It's just slightly related, but take a look at the last posts of this link:
http://forum.processing.org/topic/have-pimages-via-createimage-with-transparent-pixel

Hmmm, I did look through that thread, but I'm not seeing how it might address my question. However, I'll be the first to admit that I'm no expert with respect to programming, so if there's something specific that you see that may apply, please let me know and I'll follow up with it.

Ummm..., I said only slightly. 
Since you haven't given us any code, it's hard to advise you so.

... to detect specific pixel colours in an image and change them according to specific criteria. However, once a given pixel is changed on the display, the change is not reflected in the underlying PImage...

Well, display and PImages are separate things.
PImages are like a piece of image that you can stamp onto the display!
Display canvas changes all the time, but the "stamps" themselves are generally static.
And you should try to keep them unmodified, so you always have the original to stamp on screen again!

I believe what you really want is a detection algorithm.
There are faster ones w/ less precision and slower ones w/ high precision.
Each type of program and the shapes themselves demand different approaches for that.

Post some code, preferably full code, so we can see what's the best method to tackle that!

I don't know if I fully understand your question, but maybe you should have a look at the PImage methods loadPixels() and updatePixels(). I just did a quick test and didn't need to use those to have set() and get() function properly though. Make sure you're calling those on your PImage instance, myPImage.set(...) and myPImage.get(...).

You really shouldn't have to save every time. If you show some code it would probably be easier to figure out.

You're quite right - it was a misunderstanding. I had a loop in my code that was reloading the original PImage source. So I started overwriting the original source within that same image, which worked, but was only necessary because of the first loop. Thanks for that.