How to choose tense while using "in case" in a sentence?

The use of the Perfect Tense in Conditional clauses depends on the chronology of the events.

If the chronology is incorrect we should use the Perfect Tense.

If the chronology is correct we should use the Simple Tense.

Compare your examples:

Present tense:

Your car should have a spare wheel in case you have a puncture.

(The problem with the wheel may follow the first event, not vice versa)

I'll remind them about the meeting in case they've forgotten.

(They may forget only before the meeting, not after)

Past tense:

I left my phone switched on in case Jane called.

(She will or won't call in future)

We rang the doorbell again in case they hadn't heard it the first time.

(They didn't or did hear, we didn't know, so we rang again)