When one event in the past is a cause of a subsequent event, they are usually in the same tense, especially if you use time markers such as 'before' and 'after'.
In your examples, the illness of the lead actor caused the filming to be halted and the discovery of the human remains caused the building at the site to be halted. This is clear from both the context and the word 'after', so there is no need to use a past perfect to specify the sequencing of events. It's therefore correct and natural to put both verbs in the past simple.
NB Please do not assume that if you have two events in the past, the earlier one should always be in the past perfect. If that is what your teacher told you, you have unfortunately been the victim of lazy teaching.