If I understand correctly, as soon as you kill the NPCs in the final room then the PvP gate (Proving Conduit) will be open to use. You can then go through this, or choose to use the normal gate (Origin Conduit) back to known-space.
When entering PvP, a new timer for 30 minutes will start. There is a little more information here also, https://www.eveonline.com/article/phtxmk/abyssal-onslaught-new-content-coming-to-the-abyss