The following is my idea on how the markers, hive minds, and the convergence event work together. This is completely based only on the first two games (not including the severed dlc) and two of the animated movies. I am open to any comments or ideas and if some part of my idea conflicts with one of the books, comic or movies please let me know. Also pardon any spelling mistakes.
First we have to start with the creation of the original marker made by an unknown alien race (we will call them the aliens for simplicity). So the aliens are attempting to create (immortality, bioweapons, perfect form, resurrection, take your pick) and the end result is the Necromorphs. At first they are mindless and run around killing at random, and the Aliens who should just destroy them think that instead they might be able to control them by connecting them to a group consensus (i.e. the Hive mind). Now comes the question how to give a killing machine a mind and make it so it will follow your will? The solution was to blend an aliens mind with a necromorph body, but no simple body would do, they would need a grand monster that could truly control the necros. So they built the marker which emitted a signal to the necros and caused them to run to it and be absorbed into it to make the first hive mind. And at the final moments of its creation they sacrificed one of their own to give intelligence to the marker. But all did not go well and now the beasts had a mind and it was worse than ever. The aliens however had a backup plan in case of such a disaster, they activated the marker which in turn created a dead space field that suppressed the hivemind so they could destroy it. In the after math of the situation the aliens destroyed everything and attempted to destroy the Marker it however became sentient and defended itself violently, and so rather than destroy it they sent it off into space to be lost forever.
From here the Marker landed on earth and the rest of the story you get from the games, however I will now clarify how all of this works with the games.
The markers are designed for two stages convergence, then suppression. In DS1 the red marker that had already been activated was in stage 2, because when it was first activated it caused the outbreak, and ultimately made a hive mind by taking the mind of one of the Earthgov scientists. So the marker was then in its suppression sate when the planet was left. When the Ishimura showed up however, they disrupted the suppression by taking the marker and thus unleashed hell. The Marker being sentient wanted to go back to suppress the hive mind and thus it interacted with the people aboard the ship to get them to return it. And as evidenced by an audio log in DS2 people see different things when the Markers communicate with them. Most people went crazy or were killed but a select few (Isaac, Dr. Kyne, etc.) saw images and people that guided them along the way to return the marker. Now in DS2 the marker is in stage one and still needs to converge, meaning it still needs a mind to sacrifice. That mind is Isaac Clarke, the creator of the Marker. The marker then tries to kill him repeatedly throughout the game so it can take his mind. But the marker is smart and when direct attack fails, it acts as an ally for a time and then attempts to kill Isaac after luring into a false sense of security. Had Isaac died in the end of DS2 a hive mind would have been born and then suppressed by the Marker, but as it is he destroyed the marker and is free of its grasp so long as he isn't responsible for creating another marker.
Also the convergence event does not make an ubermorph, you can clearly see the ubermorph enter ther earthgov area with the other necros so long as you wait for a short while.
So that is it, if you have questions or dont't think I explained some points very well please just ask. And i know it was long but thanks for reading.