To Flicker:
Although Assiah was sheltered by a dome (made be sphere) shaped barrier of magic wall and surrounded by an enormous area of heavy storm.

It was still not fully impossible to come into or out of the Assiah. The most common ways were time travel and teleportation. Time travel sometime both traveled through time and place, while teleportation went directly to a different place even there were barriers.

It was also common for mistake in time travel, teleportation and casted magic of summons caused somebody to appear at the wrong place. Some of the protagonists in these kind of stories came to world of the stories from the other world. Especial in Japanese light novel, there were cases of random appeared of portal or worm hole caused this case.

Then, what would this character look like?

If he or she was time traveler, he or she may in the outfit of different era in Assiah, also may be in the outfit of the country outside the storm. Teleportation traveler would also be in the outfit of the country outside the storm. If he or she came from a different world, anything would be possible.

At last, what would the residents of Assiah through about the stranger?

Assiah seem to be a fantasy world in the modern era. Modern outfits, swords and armors co-existence. Any kind of outfit would be possible.