Regardless of where it came from, buying an engine (rotary or piston) without testing it is as risky as bungie jumping without a bungie. More so with a rotary because most people have no idea how to test them or what to look for.
There are no inherent advantages or disadvantages to USDM vs JDM. It appears you know nothing about the history of the Tii engine you bought and frankly in all likelihood it is blown or rusted inside and will require a full rebuild or it may just be scrap. You should prepare yourself for that. If your engine has a warranty, it is probably very short and requires you to install the engine and then prove it is bad and that you did the swap perfectly.
The NA to Tii swap isnt as simple as pulling one and sticking in the other. Especially if your engine is a S5 (89-91). You'll find a lot of useful information on the swaps and their various permutations at
Rotary Resurrection.
Aaron Cake has a
set of articles you might find enlightening. His article "Is My Engine Blown?" in particular will be useful. While most of it assumes the engine is in the car, the last part gives tips for testing an engine out of the car. You might also read his article "Removing An RX-7 From Storage, Dealing With Improper Storage" and skip down to the section on dealing with a car that has been improperly stored as the Tii you bought almost surely has been improperly stored.
Good luck. Don't panic and remember that money solves all problems!