There's a big difference between driving 5-10 miles at low speeds on an emergency space-saver spare and driving 20K miles at normal highway speeds.
IIRC, the Miata owner's manual says to put the space saver spare on the front for cars with Torsens (and move the front tire to the rear if it's the rear that went flat).
The concern isn't the transmission like many 'less aware' mechanics think. The concern is the increased rate of wear on the diff/s. If you have clutch based LSDs then it will use the clutches up at a very fast rate. If you have a Torsen it won't use it quite as fast, but they to are capable of wearing out (mine has, though from use not different tires).
The gears and/or clutches inside a diff are not designed for constant velocity, but low speed sporadic movement in both directions. With two different sized tires you are looking at constantly going one direction 100% of the time.
All in all though, 99% of all cars/SUVs are able to deal with these small discrepancies without even noticing. But there are a few vehicles out there with lockers and heavy duty diffs that do not take well to this situation, and have spread their story like a wildfire in the plains of Utah.
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