Stop component updates on recompute

Dear all,
I want to implement a component that prevents down-stream components to execute.

I found this post which is close to the subject in question: How to trigger updates down only selected outputs of component?.

For normal updates - when e.g. an up-stream components changes - this works. However in case of a recompute of the whole document or when the document gets loaded, this method fails.

I tried to change the Phase-property of the down-stream components without success.

Is there another possibility to prevent down-stream updates in the above described scenario?

– Clemens