I ran into some quirkyness with lined custom transformers today\\

Normally, when one has a workspace with a linked custom transformer, and you change the stuff between the input and output ports of that transformer, the next time you run this workspace uses the new functionality. That is when you save the transformer and don't make a new version.

The parameters of the linked transformer are not changed. Obviously that goes for the published parameters, you set in the workspace through dropdown menu's etc. on the linked custom transformer, but it also seems to go for the private parameters of the linked transformer.

It looks like they are stored in the workspace as wel in some sort of way.
When you have changed these during the rework on the Linked transformer, still the old private parameters seem to be used when running the workspace!

In my case the private parameters were python-scripted parameters in the linked transformer. I changed the python-scripts. When running the workspace with the transformer, still the old python-scripts were run!!!

The only way to get the new scripts to be executed was to delete the linked transformer, and drag it into the workspace anew from the transformer-gallery.

I found this on FME 2016.1 build 16494 - WIN64. I have not yet found any documentation describing this kind of behaviour. Allthough the parameter behaviour is consistent accross all custom transformer parameters, I doubt if this is the thing one would expect to happen. Keeping the private parameters of a linked transformer private to that transformer seems more logic to me.