I'm going to go slightly against the grain. The parts that I do agree with are that he is likely a conflicted/confused 20 something year old and it's coming out, in part, in this gift giving "debate". I also agree that you and your DH let him know that you are in no way intending to make him feel obligated to give you gifts and ask him to tell you how we wants you to communicated family events to him in the future.
The part that I'm not totally on board with is DS's birthday. I sort of see his point. It doesn't seem like he was being invited to a birthday party (which would be a gift giving event), but just 'reminded' that this date was coming up. I don't think that birthdays, by themselves, are necessarily gift giving events. In some families, yes...but, if he never gives gifts to his other brothers, then I assume this isn't a family tradition he's accustomed to.
It's nice to want to include him in on these things, but as an adult he doesn't need to be reminded that it's his little brothers birthday or told to call. And I do think that even if it's unintended, mentioning that you already have a gift and offering to put his name on it, does communicate that you expect that the older brothers do give gifts to the younger one. And try to imagine where Jeff is coming from. His parents aren't together (don't know how young he was when that occurred) and now he has two sets of blended families to contend with. If his parents didn't spend his childhood making sure that the brothers all acknowledged each other's birthdays and suggested calls, gifts, special recognition, or whatever, then he could feel slighted. At least I wouldn't blame him if he felt that way.