You can use the past simple even for specific actions that are complete. You can use the past simple in half of a sentence, and past perfect or present perfect in the other half. You can mix them up, as long as it works semantically, and as long as each use is correct in and of itself.
A lot of the time, there's more than one verb structure/form (or 'tense', in common parlance) that can be used in a given situation. Simple forms can often be used where a perfect or progressive aspect can be used. Sometimes only one is natural even though multiple ways of doing it are valid, and you just have to learn those by experience.