Is it possible for a parasitic wasp to alter the behaviour of its host after emerging from it?
The species of wasp in the video you link to is Cotesia glomerata. Furthermore, there is at least one other species, Glyptapanteles, which parasitizes other caterpillar species in the same way and induces the same behaviour in its host.

I'm not sure which virus it is.

http://www.newscientist.com/article/dn14053-zombie-caterpillars-controlled-by-voodoo-wasps.html?feedId=online-news_rss20

Is it possible? Of course, you have an example! Though, there is a small caveat. Some of the offspring sacrifice themselves to induce the behavioral change after the rest of the brood has emerged.

Is it common among parasitic wasps? No. While injecting offspring into host species is a common theme for parasitic wasps, and while there are a handful which somehow induce behavioral changes in the host animals - continuing the manipulation after leaving the host animal is extremely rare among parasites in general.