Hi @itonewbie 
We're working towards making all Intuit accounts to be synced. One account and one sign-in for multiple products or URLs is working as designed. 
Logging into the community will not log you into your ProConnect Tax online account unless you are already signed into your ProConnect Tax account. 

I agree that logging out of an online account manually is a great practice for security. Meanwhile, I'll do some research on the inactive logout time frame for ProConnect Tax. 
Thanks for reaching out!