The rationale behind this is that
Tyrannosaurus is more closely related to
Tarbosaurus and
Zhuchengtyrannus than it was to other North American tyrannosaurines. Furthermore, these Asian tyrannosaurinins are older than
Tyrannosaurus. So the hypothesis is that this lineage of tyrannosaur originated in Asia, and the ancestor of
Tyrannosaurus migrated into North America before the late Maastrichtian.
The spread isn't a problem: once a taxon makes it from one continent to another it can spread to the limits of its mobility and habitat in relatively quick periods. We see the same when Cenozoic mammals crossed Beringia either direction, or when they crossed the Isthmus of Panama.