Yeah this is very odd for sure.
One thing i've seen before is if you're using knock off brand batteries, make sure that they do not have any tape "residue" on them that would make a bad connection contact, and it is possible that even though you may not have used the knock off brand batteries before, that one of them may be DOA (dead on arrival).
So it's possible that one of the batteries may be dead, while one is fully charged, causing inconsistent results while doing your testing.
I say this only because I went through this and spent an entire night dealing with these damn "sticky batteries" ... enough to where I named one of my live mixes after it LOL. And that wasn't all, some of them were dead when I got them, so you can imagine my frustration that night ....
It is possible that NEO turns on with those same batteries because it allows the chip to function at a lower voltage (as batteries start to die, the voltage goes down), but i'm honestly not sure what the setting is with Primer, maybe John can chime in on how that works?
You should also check to make sure that the batteries are actually making a good connection (this is normally the issue outside of dead batteries) ... I've had some cheap batteries where the bottom part of the battery was a little more recessed into the battery, causing numerous issues when trying to get them to work.
So make sure that when you're putting them in that they make a good connection, both on the top and the bottom. Make sure the battery holder hasn't been bent or anything causing a bad connection.