As I'm currently reading through the Avengers books from this time frame:
Reed's participation with the Illuminati in NEW AVENGERS was due to his having a back-door to contact Earth that he didn't tell the rest of the FF about. He was, indeed, on that search for a cure to his condition; however, the impending destruction of the universe was worth a few minor interruptions.
In AGE OF ULTRON, the FF returned to Earth after Ultron had taken over, and only Sue survived. Once the timeline was reset, of course, none of that needed to happen, so it didn't.
One of the reasons Tony pushed for the expansion of the Avengers' roster seen in AVENGERS at that time was to help free him up to spend more time dealing with the incursions. In fact, he was one of the few Avengers who did not go into space to fight the Builders in the "Infinity" storyline, precisely so he could stay on Earth to deal with incursions.
I've gotten the impression that, possibly, the multiple time travel trips seen in AGE OF ULTRON are connected to the collapse of the Marvel multiverse. While it's not the only possible cause (the events happening out in the universe during "War of Kings" and "Realm of Kings" definitely ripped a hole in the universe), the strong warnings and concern about using time travel to fix the problem, followed by the fact that there were multiple trips by the same people to the same time, seems like a strong candidate for causing major problems. This is certainly not explicitly stated anywhere; I simply feel like it was being hinted at.
Looking at your specific question, it looks like you're asking about the first storylines in Jonathan Hickman's runs on AVENGERS and NEW AVENGERS, and AGE OF ULTRON. If I had to try to place those on a timeline, I'd tend to put NEW AVENGERS 1-6 first, then AVENGERS 1-6, then AVENGERS: AGE OF ULTRON.
- As I noted, one of the reasons Tony promoted the expansion of the team was the threat of the incursions.
- AVENGERS requires that the selection and organization of the new team have all happened. Logical, all this would have been going on while the Illuminati (inclkuding Steve Rogers at that point) were figuring things out from their end. Hence, the first storyline in AVENGERS following the first storyline in NEW AVENGERS.
- AGE OF ULTRON didn't start until we were already well into the other two storylines. Therefore, place it after they conclude, as that's the simplest solution. Since Ultron's attack, in the final version of the timeline, wasn't really that much of a threat overall (no worse by comparison that some of his other attacks, certainly), there wasn't much discussion of it in the other books outside of the .AU issues.