System Information
Operating system: Linux-5.17.5-76051705-generic-x86_64-with-glibc2.31 64 Bits
Graphics card: NVIDIA GeForce RTX 3080/PCIe/SSE2 NVIDIA Corporation 4.5.0 NVIDIA 510.68.02

Blender Version
Broken: version: 3.1.2, branch: master, commit date: 2022-03-31 17:40, hash: rBcc66d1020c3b
Worked: (newest version of Blender that worked as expected)

Short description of error
A material with a custom object on Texture Coordinate node will have its coordinate left behind when instanced from a collection even if you parent the custom object to the material holder.

Exact steps for others to reproduce the error
Add an Empty;
Add a Material to the Default Cube;
Add Texture Coordinate Node and set the Empty as Custom Source;
Plug the Object Output to the Material Output and preview the Shading.
Parent the Empty to the Cube just in case;
Move the Cube;

Here it's all correct. The coordinate keeps relative to the Cube as expected as the Empty is being transformed along with it.

Now the problem:
Instance the collection where the Cube and the Empty belong to;
Move the Instanced Collection.
Result: The coordinate does not move along with the Empty within the instanced Collection.

sample files:

video:

I'm not 100% sure if this is the expected behavior but this seems a very dangerous workflow and counter intuitive if you plan to instance something created like that.