sessionStorage is scoped per-tab.
There are a bunch of ways we could have resolved that problem, all with subtle bad behavior in some cases. We opted to have the prerender and the original tab share session storage, and not allow use of a prerender in other tabs. You can still get somewhat funky session storage behaviors if you really try.
I'm not sure what option IE opted for, but you can undoubtedly get different subtly broken behaviors with their implementation of prerender + session storage if you try. The two features just aren't compatible.