I was at war with the Festron Hunt. When I started a new turn I saw what is shown in the screen snapshot below. The pink area shows the area of influence for the Festron Hunt as shown by the Influence popup. However, the 2 core worlds that used to belong to the Festron Hunt now appear to belon to the Mimot Brotherhood. Also, all of the starbases and shipyards that the Festron Hunt had have all disappeared. What I suspect has happened is that the Festron Hunt surrendered all of their assets to the Mimot Brotherhood during their turn, but the game did not update influence for the cells that had Festron Hunt influence. I also have not yet seen the message that appears to announce that a civ has been defeated.
Update: At the beginning of my next turn, the message shown in the second screen snapshot below appeared.
Recommendation: When a civ surrenders, do all of the necessary updates (worlds, shipyards, starbases, and ships already update correctly, influence does not) and show the civ defeat message at the beginning of the players turn (not the NEXT turn). Note: an item DOES correctly appear in the Monthly News Report immediately after the defeat of the civ.