The cache for the invasion quests (Complete 4 specific quests in that area) are still rewarding ilvl 370 gear, and it is was said to be increasing to ilvl 400 in Season 2. Wanting this to be changed in time to be able to turn the quest in before the invasion is over.
I think there has been a little miscommunication on some of this. This is fromt he official post, stickied in the General Discussion forum:
It does not mention invasions. People asked about them in the thread, there was no answer.
Another thing to note, Azerite pieces from assaults are not updated to contain 5 rings despite its 370 ilvl. As aforementioned hopefully it will change in the future
That’s right, from the same post:
Doesn’t mention assaults.
My assumption on this is that since assaults were added in 8.1, they don’t need to be updated to season 2 = 8.1 levels. They are already at the level they intended them to be. We just got to have a month of them seeming high level in the between-seasons period.