If you are seeing this message, then it is very likely that something is messed up. CS6 should have an activation process. It should work irrelevant of your now out of date CC account. But it doesn't appear to be doing that for you. Contact Customer Service before you are locked out. It may be that you won't be locked out, but do you really want to wait incase, it happens.
The present activation and account system doesn't work well. I have TCS on my PC with Photoshop CS6 (I believe). It should not be contaminated by my CS6 MS and CC software on my Mac. But it seems to get counted as an activation on my account. Go figure. I am only suggesting preventative action in case it bites you. I am not customer service nor technical support. I can only give you advice based upon my experience.