When we first tested 15.3, that was one of my questions to CA-- that if we leave that portlet, then users are directed to the Classic, thus both new and classic can be used in the same instance, Though I think this was a design oversight they did tell me that you should be able to change the hyperlink in the portlet. I never got around to testing that, but will be in the near future on 15.4
also , if anyone has their homepage set to timesheets, then if you activate the new timesheet ux, they too will go to the classic. CA told us that we would have to reset all users, if we did not want them accessing the classic at all.
note- in my testing, I was able to break timesheets (get errors) by using both classic and new.. just an FYI