J'étais content qu'il vienne: the main verb does not decide

A past main verb changes nothing

This is the trap, because it looks like the backshift in reported speech and behaves nothing like it. Put the main verb in the past and the clause still times itself against the main verb.

Both are correct modern French, and they mean different things. A past main verb never obliges you to write a past subjunctive.

Two tenses, not four

Reference grammars list four subjunctive tenses. Everyday modern French uses two, and lets them cover for the other pair.

You still need to recognise the old pair in older literature and in writers who enjoy the effect. A third-person verb ending in -ât, -ît or -ût with a circumflex, straight after que, is usually an imperfect subjunctive (the exceptions are ordinary presents such as qu'il connaît and qu'il plaît): read qu'il vînt as qu'il vienne and carry on. You do not need to write one: outside deliberately literary prose it sounds stilted.

One subject: the perfect infinitive

When both halves have the same subject, French drops the que clause and uses a perfect infinitive: avoir or être in the infinitive plus the participle. This is the same-subject rule, applied to a finished event.

In the negative, ne pas usually goes in front of the whole infinitive: de ne pas avoir répondu. (Formal writing also has de n'avoir pas répondu.)

Mistakes English speakers make

And do not match the main verb: j'étais content qu'il vienne is right when he was still on his way.