Whether is is extended or not depends on the serial number for perpetual licence. The subscription model has only extended version.
Don't see how it would be converted, unless you have mistaken the CS6 version you get with CC for the licence version.
Hope this helps.
Thanks Curt, but I don't believe you're correct about the subscription model having only the extended version, at least according to the cloud updater app on my PC. Both versions ( 32 bit and 64 bit ) of CS6 on my machine are at 13.0.1 Extended and the CC updater indicates there are updates to 13.1.2 for both standard and extended versions. I'm not sure why the CC updater app would even attempt to update the perpeptual license version, unless I've totally misunderstood CC. (totally possible BTW). I never purchased PS CS6 Extended in any form, so it seems it had to have been installed by the cloud updater.
CS6 should not remain a perpetual version as you are already having CC membership for Ps CC activated.
This is expected behavior.
PS 13.1.2 is a subscription patch(for Creative Cloud users) not for perpetual, this would not get applied over 13.0.1.x(update for perpetual). As you have 13.0.1.x already applied then you need to re-install Ps CS6 to get Ps 13.1.2.