TL;DR: You must enter a valid 2012 R2 key into the 2012 R2 instance and a valid 2016 key into the 2016 instance.
Long version:
Key != license != activation.
A key is an alphanumeric series entered into the product key prompts. It is always version-dependent, 100% of the time. A 2019 key will not work on 2016 or vice versa or any other combination. A key does not indicate anything except digital housekeeping.
Windows Server Standard cannot activate any guests, ever. AVMA is a product feature, not a key or a license. That feature is only found on Datacenter and only functions when a Datacenter edition hosts Windows Server guests. Even then, the key entered into the guest is still version-dependent, 100% of the time.
If you have a legal license to operate Windows Server on a given piece of hardware, then it conveys a particular set of virtualization rights. Unless you have a modified license (e.g., OEM), then it grants you downgrade rights. This has absolutely nothing to do with any keys. In some cases (usually OEM) you wind up with a legal right to run operating systems for which you have no keys.
Summary:
- No key issued for Windows Server 2019 can be used to activate a Windows Server 2016 or Windows Server 2012 R2 guest. Period.
- Windows Server Standard does not have the AVMA feature and cannot activate any guest. Period.
- In order to exercise downgrade RIGHTS on a down-level GUEST, you must still enter a product KEY that matches that operating system version. Period. There is literally no situation in which this is not true, not even under AVMA.
In other words, the rules for a guest are the same as for a physically-installed OS. A Windows Server 2019 LICENSE allows you to use Windows Server 2016 as your management operating system if that's what you want, but you still have to enter a Windows Server 2016 KEY.