The Puppeteer enters the Marionette's body, as in, physically vanishes into them.

... I'm trying to decide if there would be a particularly evil/unsettling way to have this look.

Also, when a Doll rips a Puppeteer out of a Marionette, they literally reach into the Marionette(not actually damaging their body, though), grab the Puppeteer, and rip it out.