The reason for the Tucano having 'stick central' in the spin recovery is due to the fact that it has an inverted spin mode as well as the erect spin mode, and 'stick central' works for both. Therefore, the spin recovery is identical for an erect and an inverted spin and a pilot does not have to identify whether the spin is erect or inverted in order to effect a recovery.
So can other, supposedly relatively benign aircraft. For example, the JP3 and the Cessna 150.
I saw the latter with an instructor (spin training was included in PPL training back then) and during entry to what was supposed to be a normal spin, the aircraft flicked, the prop stopped, and suddenly the ground was "up").
I also managed to get myself into an inverted spin during solo aerobatics on the JP3 BFTS course. I was lucky to come out of that, the last thing on my mind at the time was ejecting and after I recovered to a climb I realised I was well below minimum abandonment height.
The Chief Instructor at CFS at the time I was there (late 80s) wrote an interesting article in Airclues. He was current on either three or four different types of aircraft at the time, all with different recovery techniques (Hawk, JP, Bulldog, possibly Chipmunk). One day he was flying a VSO (the AOC, iirc) on a GH sortie in a Hawk. The VSO asked to see a spin. As the CI entered the spin, for a few very worrying seconds he realised he couldn't remember what recovery technique he should use for the type! The point of the article was to know what you're meant to do and if possible pre-brief your recovery actions.