Short answer: Samsung.
Long answer: TSST is a joint venture between Toshiba and Samsung (Toshiba Samsung Storage Technology). For most consumer drives released as a TSST-branded drive, marketing, support, and firmware updates are handled by Samsung, while Toshiba helps with the underlying technology to some degree. There are some old drives made exclusively by Toshiba and marketed as such, and there are some marketed by Toshiba but are considered to be rebadges of the TSST/Samsung equivalent; in either case, those would be identified strictly as “Toshiba” when connected to the computer. Samsung’s drives have pretty much identified as “TSSTcorp” ever since the joint venture was created, and only under certain circumstances would you see a Samsung drive identify itself as “Samsung” (maybe some drives from around 2000?).
These days, Toshiba doesn’t really release optical drives under its brand name, leaving Samsung to do that.
And just like every other optical drive manufacturer, they do not necessarily help out with drives in pre-built machines from big vendors like Acer. Optical drive manufacturers tend to rely on the computer vendor to provide all support.