The visa requirement is created by a separate sub-paragraph in the relevant article of the Schengen Borders Code, which reads:
- For intended stays on the territory of the Member States of a duration of no more than 90 days in any 180-day period […] the entry conditions for third-country nationals shall be the following:
(b) they are in possession of a valid visa, if required pursuant to […]
There is no separate regulation, not even a distinct article, laying out entry conditions for “visa nationals”. To the extent that you are really exempted from the visa requirement, all the other rules should therefore still be exactly the same.
Regarding the maximum length of stay rule, see How does the Schengen 90/180 rule work? According to the calculator mentioned there, your stay is exactly 90 days long so it should be allowed but you would not have even a single day left until December.
I must however add that any visa exemption for special passports would have to result from some other agreement or national rules (as pointed out in the comments by @phoog) and it's possible those rules would also create an unusual regime regarding the maximum stay for Turkish special passport holders. I don't really know about that.
(Yet another) EDIT: I am told that only some (but not all) Schengen countries grant Turkish special passport holders visa-free entry. I can't provide any details but you ought to double-check the rules for each country you want to visit because that's apparently not as easy as you thought.