Yes, your statements are correct.
If you are running SRM and/or vCenter on Windows 2012 in a VM on ESX 5.1 U1 you are in a non-supported configuration. So, yes, you need to first upgrade ESXi to 5.1 U2 in order to run Windows 2012.
After that you can run vCenter and/or SRM on Windows 2012. SRM also supports VCSA (vCenter Server Appliance) which is Linux-based version of vCenter.
Also, you are not required to upgrade all your ESXi hosts to U2 (but we recommend it). You need to only upgrade those hosts that are going to run Windows 2012 VMs.
Best Regards
Stefan Tsonev