Please read the following sentence and explain to me why is it possible to mix past tense "decided" as the main verb with present perfect "must have rendered" in the same sentence?
They decided that her grief must have rendered my friend lonely and confused.
"must have rendered" is not 'present perfect.' It is a modal form in the perfective (meaning 'before'), in this case 'before they decided.' It is a logical conclusion about what had happened before the utterance.
"I told him he must have made a mistake."
"I told him he had made a mistake."
"I told him he must come (the next day)."
which is about the same as:
"I told him he had to come (the next day)."