"Correct pronunciation" isn't a definite single thing. The pronunciation of -ci-, -si-, -ti- before a final unstressed syllable in such names is fairly variable. The following pronunciation variants are all within the norm.
The spelling -ci- can correspond to /si/, /ʃi/ or /ʃ/.
The spelling -si- can correspond to /si/, /ʃi/, /ʃ/, /zi/, /ʒi/ or /ʒ/.
- The pronunciations /zi/, /ʒi/ or /ʒ/ are only possible after a vowel, or for American English speakers, after /r/.
The spelling -ti- can correspond to /ʃi/, /ʃ/, /ti/.
/ti/ is not very common, and many names seem to lack variant pronunciations with /ti/. But some pronunciation guides, e.g. The elements of Latin grammar, Richard Hiley (1849), suggest that /ti/ is to be expected in Greek words/names. That would favor the use of /ti/ in "Leontius" (Greek Λεόντιος).
After "s", "ti" cannot be pronounced as /ʃi/ or /ʃ/. Instead, the possible pronunciations are /ti/, /tʃi/ and /tʃ/.
There is supposed to be a rule (mentioned by Hiley) that "tti" is pronounced /ti/.
After "n", some speakers have no distinction between /ʃ/ and /tʃ/, so they might use /tʃ/ instead of /ʃ/ in words spelled with -nci-, nsi- or -nti-.
Other pronunciations of these spelling patterns exist, but it's probably safe to classify them as irregular/exceptional. E.g. -ti- is exceptionally pronounced as /ʒ/ by many speakers in the word equation, and as /si/ by some speakers in the word negotiation.