It's just a simple lore question. I hear constantly hear about the dragon crisis in Skyrim, so at the same time are dragons affecting other provinces of Tamriel? It seems like an obvious answer, but everything I see says specifically Skyrim and not Tamriel.

The return of the Dragons is Skyrim only, for the moment. Not to spoil things but the main plot spells out a fair bit about the whole return early on, so you should play through some of it at least.

It seems to just effect Skyrim, no where else, it's illogical though, they're giant flying beasts but yet they seem to limit them selves to Skyrim.

Well, one could hope they BBQ'd a few golden marshmallows in Summerset but I doubt it... *sigh*