I did what you advised and both devices showed 6 different numbers.
Have you tried using these new 6 digit codes generated by your second device to access the accounts in questions?
Does the 16 digit key need to be in capitals or lowercase?
It shouldn't make a difference since they are Base32 strings, but I suppose it depends if you are using a buggy app. I have always seen them displayed as all uppercase, though. On Aegis, it doesn't matter if you enter lowercase or uppercase, they both generate the same 6 digit codes.