Detect Magic would not work on the creature, but may work on items on that the creature is wearing/carrying
Detecting magic on the creature wearing it
The quote you provided for the Amulet describes what it does - and it makes any magic currently active on the wearer hidden from divination magic.
Detecting magic on the items carried by a creature
At first pass, it does seem like detect magic should work here. But I think this is going to be up to some DM decision-making. Most of the time, items carried by a character are often considered part of their character (for instance, magic that causes fire generally stipulates that it won't burn things carried or worn.) However, that is a specific rule and may not be applicable at all times.
It's also important to note (thanks miniman!) that in order for detect magic to detect, the item must be visible. If it's not visible, then the spell definitely won't detect it.
In general, it does seem like divination magic won't hide magical items carried/worn by a character. But as with the fire example above, I think there is a case that it will hide those items. I think it's more fun that someone wearing this amulet is basically covering themselves and everything they've got in this magical protection.
Your table, your rules
The only thing that really matters is that the spell doesn't work to detect items worn or carried, then that's fair to rule, but just remember to be fair, fun, and consistent if this sort of thing happens again.