Check the version number of the installed CS6 version of Photoshop. If it is greater than 13.0.6 (for example 13.1.2), then the CC update mechanism has converted your CS install into a CC install version of CS6 and tied it to the CC license.
IMO, I'd keep 13.0.6 and not upgrade it. For example, you want to move your CC activation over to a third Mac or PC, the CS6 is a permanent license version that you can use when your CC license is deactivated.
I use Windows and CS6 version 13.1.2 is slightly different then perpetual CS6 Version 220.127.116.11 windows. It also in my case enabled me to use the extended features. I'm sure if I drop my subscription I will have to remove all creative cloud software including CS6 version 13.1.2 and then install perpetual CS6 and I'll be back to my perpetual serial standard edition at version 18.104.22.168 windows.
The differences between Mac Perpetual 13.0.6 and subscription 13.1.2 should no be much different. Windows perpetual was still able to use optional CS5 Plug-is which were available in 32bit and 64bit Photoshop but only available for 32bip Mac Photoshop. CS6 Photoshop Mac is 64bit only so mac users could not use the optional CS5 plug-ins like Web Photo Galleries and Picture Package.
OMG, you gave me a little heart attack there! haha
I just checked and fortunately my Adobe CS6 Extended is in fact version 13.0.6
I'm getting pretty annoyed with Adobe pulling these underhanded tactics :\ (or if they're not doing it on purpose to trick users into using CC products and getting rid of their legacy products, then that's just very poor design). I love Adobe's products but they're handling this whole CC business extremely poorly. I mean, I was already extremely annoyed that I had to create a separate Adobe account just to activate my Lightroom 6 (not even that long after its release) and was very disappointed with the discontinuation of the perpetual licensing/CS plans, but now this? But what do I know, I'm just a user/customer
I know it's probably not gonna happen, but is there any chance there'll be an update to lightroom 6 so I can actually have it associated with and activate it with my main Adobe account?
Even if you accidentally installed 13.1.2, you could uninstall it and reinstall your permanent license version.
As for Lightroom, go to their forum and I'm sure they know more than me.