I'm not surprised but haven't tested it myself.
Project deployment model packages are deployed using ISDeploymentWizard.exe and there is a version associated to each version of SQL Server (and bit-edness).
For example, one laptop here has VS 2013/2015 installed and SSDT for 2012/2014/2016 installed. If I look for that executable, I see
- C:\Program Files (x86)\Microsoft SQL Server\130\DTS\Binn\ISDeploymentWizard.exe
- C:\Program Files (x86)\Microsoft SQL Server\120\DTS\Binn\ISDeploymentWizard.exe
- C:\Program Files (x86)\Microsoft SQL Server\140\DTS\Binn\ISDeploymentWizard.exe
- C:\Program Files\Microsoft SQL Server\120\DTS\Binn\ISDeploymentWizard.exe
My new machine only has bits for 2017 and looks like
- C:\Program Files (x86)\Microsoft SQL Server\140\DTS\Binn\ISDeploymentWizard.exe
- C:\Program Files\Microsoft SQL Server\140\DTS\Binn\ISDeploymentWizard.exe
The other thing to factor into all this is that using a newer version of the SSIS tooling (ISDeploymentWizard, dtexec, dtutil) will happily roll your version forward to match its version. Which is helpful as a consultant to upgrade things but the devil when you want to use new tools against old code.
My guess is that SSMS is defaulting to an ISDeploymentWizard that is not in the 120 folder. Unfortunately, I don't see a parameter in the deployment wizard to address version.
/Silent[+|-] Default value:'-' (short form /S)
/SourceType:{File|Server} Default value:'File' (short form /ST)
/ModelType:{Project|Package} Default value:'Project' (short form /MT)
/SourcePath:<string> (short form /SP)
/SourceServer:<string> (short form /SS)
/Packages:<string> (short form /PK)
/ProjectPassword:<string> (short form /PP)
/DestinationServer:<string> (short form /DS)
/DestinationPath:<string> (short form /DP)
/SkipSource[+|-] Default value:'-'
@<file> Read response file for more options
Your best, yet icky, bets are to
- Keep a copy of SSMS for SQL server 2012 lying about for deployment
- Deploy from SSDT 2012
- Deploy from the commandline explicitly defining the source exe
The last option is actually that bad. Use the GUI to click through the deployment but on this screen, stop

That highlighted box is selectable/copyable. DO THAT. The command line deploy has been built out for you (excluding the part that says "Command line:")
Thus you'd have something like
"C:\...\1XX\DTS\BINN\ISDeploymentWizard.exe" /SILENT /SourcePath:"C:\MyProject.ispac" /DestinationServer:"localhost" /DestinationPath:"/SSISDB/Folder/Project/MyProject"