I've been playing as the Advent and have discovered on multiple occasions that my culture will not dominate enemy AI occupied worlds. It works fine on minor factions, but I cannot get it to work on planets that are occupied by a player. In my screenshot below, I have culture coming from two neighboring phase lanes and have used proselytize on a planet (with no broadcast center) and my culture will not begin to dominate the planet. This is a huge issue as it renders the Advent's Conversion mechanic useless.