Son mari a économisé en cachette

Bonjour Tuhin P

The husband saved for the trip furtively, sufficient to cover all expected costs.

Once he had done that, the action was complete.

So we have an action carried out historically and completed.

He was not saving continuously but only while he gathered sufficient funding for the trip.

Passé composé is therefore appropriate.

I hope that this helps.

Bonne continuation 

Jim