You can get ATF SPIII from Mitsubishi . I got some this week $42, 5Litres.
In the Mitsubishi forums I'm reading of people using Castrol Transmax Multi Vehicle for SPIII.
My local Hyundai dealer when asked about genuine fluid told me his system showed AC Delco Multi Trans Fully Synthetic DEXRON III A.T.F. being used.
Said they do not sell it.
It's a multi Make Dealership so I don't know if this is a Hyundai recommendation or what they use but must be ok given the long warranties new cars carry.
SPECIFICATIONS:
JASO M315 TYPE 1A
SUITABLE FOR USE WITH FOLLOWING SPECIFICATIONS:
AISIN WARNER / AW-1 BMW MINI 83 22 0 402 413 / 83 22 7 542 290 CHRYSLER ATF +3 / +4
DAEWOO DAIHATSU ALUMIX ATF MULTI DEXRON III
FIAT TYPO T-IV FORD MERCON / M2C924-A / M2C922-A1/ 95LE GM 9986195
HONDA ATF Z-I HYUNDAI SP-III/IV ISUZU BESCO ATF-II/ATF-III
JWS 3309/TYPE T-IV JATCO 3100 PL085/ FWD (N402) / JF506E (K17) KIA SP-IV
MAZDA ATF D-III/ATF M-3 MITSUBISHI SP-II/-III NISSAN C/D/J
SAAB 3309 SUBARU ATF OIL/ATF OIL SPECIAL/ ATF HP SUZUKI ATF 3309/3317
TOYOTA TYPE D-2/WS TOYOTA TYPE T/T-II/T-III/T-IV VW G 052 990/055 025