I was also really confused about why the mod page says it supports Procedural Parts, but in reality it doesn't. So, I did a little bit of investigating. I figured it must've been supported at some point, so I went to SpaceDock to find past versions. And what do I find in version 2.4.2? (That's around the release of 1.4, 2018)
Why? I haven't got a clue. I pulled up the version of Configurable Containers from immediately before that update, and did the same for Procedural Parts. When comparing them to the new version, the only relevant difference in CC is that there's a config for PP. On PP's behalf, almost nothing had changed; the only difference was the change of 'TECHLIMIT' to 'UPGRADE'. Comparing other files from within CC, the formatting there hadn't changed either, besides a change in the Module Manager call in the new version to make sure that other fuel switch mods and CC didn't overlap.
The PP config had some extra parts in it, which become totally meaningless when you consider that one tank can be modified for anything, so I deleted everything but the patch to the procedural fuel tank, and put it in with the rest of the configs in the new mod. And what do you know, it works.
Absolutely nothing changed between versions, and CC and PP still work together if you just use the old config. I am utterly confused as to why Allista dropped support for it.
Here's a link to my version of the Procedural Parts config file. Just drop it into \GameData\ConfigurableContainers\Parts and you should be good to go. This only covers the procedural liquid fuel tank, of course. I might update this later, because I'm probably going to add support for the procedural nosecone at some point. Also, because I didn't add the same anti-fuel-switch-mods incantation as the rest of the configs do, you might run into issues if any other fuel switch mod also modify Procedural Parts.
I (in my admittedly limited testing) haven't experienced any serious conflict with TweakScale so far. I haven't been able to switch tanks in flight, but I'm not sure if that was because of TweakScale or because there were other (unmodifiable) resources in the part. If there was a problem, one of the game updates since this was posted may have fixed it (my version being 1.12.3).