The expression comes from a well known nursery rhyme:

ainsi font, font, font, les petites marionnettes.

The person singing is moving his hands simulating the puppets and when the following verse ends:

Trois p’tits tours et puis s’en vont

he hides his hands under is back and the baby laughs out loud.

In your examples, the metaphor is : after the show, a puppet disappears, i.e. after five years of marriage, one of the spouses is suddenly leaving.