As long as there is no suspicious behavior, you should be okay. That means NO CLICKS on either site from that computer. If it were I, I'd make sure there were no links between the sites in the accounts either - *nothing* that might raise a red flag.
I manage at least five accounts from one computer, one for me, one for my company, and three for clients. Never had a problem.
I run 2 accounts from the same computer (both me, but one business one personal). The sites on those accounts do link to each other.
I would imagine if one account were ever banned then the second account would also be banned as a related account. I would worry about managing accounts I had no control over through the same computer for that reason.