In most contexts, a 'parallel universe' would refer to the concept from science-fiction. There may be many differing versions of the concept throughout fiction, and while it is generally considered to be entirely fictional there are some aspects of the concept that are borrowed from the theoretical framework known as string-theory. Additionally, there are some credible scientists who argue for a 'multiverse' theory that bears some similarities to parallel universes in fiction.
Most fictional concepts of 'parallel universes' suggest that there are other universes that run parallel to our own, not occupying an adjacent space that can be travelled to by conventional space-travel, but either in a different 'bubble' or existing on a different 'frequency'. In many science-fiction stories, parallel universes bear resemblances to our own but may have diverged at some point in history convenient to the story. A common trope in parallel universe stories is that a historical war, such as WWII, was won by a different side therefore creating a different 'branch' of history.
In your example though, which does not appear to be science-fiction, it seems to be used figuratively to mean someone in a parallel position (ie fulfilling the same role) but in a different place (perhaps a different country?), in which case 'universe' is not literal but being used to perhaps show that the two 'worlds' in which the persons inhabit are so far apart.