I would be willing to admit stupidity in not noticing a logout button somewhere near the continue button, perhaps a kind soul would be willing to offer some information either way?
The way I understand is that Cryptic handles Paypal interaction like any other company:
You're redirected to a PayPal page, where you log into PayPal's servers
On PayPal's server, you enter your payment information and address
You submit it and get a brief "confirmation" page for your payment saying something like "Your payment has been received"
This is your chance to log-off, usually
That said, from an IT standpoint, I'd be very worried if Cryptic were able to log you on/off of PayPal's Servers. If third parties are able to change your log-in status on a transaction that is just between you and paypal, there's a big issue.
PayPal acts as a middle-man. Technically, then receive your payment and pass it on to Cryptic via their secured servers. Allowing anyone to change that private transaction between you and them would be very sketchy indeed.
There's no confirmation page after completing the transaction? That sounds fishy.
Edit: This is an example from buying C-Points starting from the ingame C-Store:
Basically, if I wanted to buy C-points for example, I would be directed to my account to log in, then select how may points I want to buy, then payment method which in this case is PayPal, after confirming my details and continuing, STO will automatically redirect to PayPal which requires the user to first log in, then a Transaction page is shown detailing what you are buying - basically an invoice of sorts. At the bottom of this page after reading the details are correct the user confirms the transaction and upon this action is automatically redirected back to their STO account. It's at this point PayPal should log the user out automatically after completing the transaction.