Explanation

Just on the second thought.

There are few references, but I'm inclined to think that the version "осторожная ферментация" deserves a serious consideration.

In Italy, where i live, and drink, we call it "un'attenta fermentazizione".
What it refers to is not "thorough" (тщательная), but exactly "careful" as осторожная. For sure, the expression Thorough Fermentation exists too (and then it's тщательная).

The common concern is excessive fermentation (in fact, too "thorough", in a way, hence not very careful!), increasing too much methanol and tannin content and making the final product too aggressive. It often happens with such "heavy" varieties as, for example, Merlot.

So, "careful fermentation" (осторожная ферментация) may even be interpreted as somewhat opposite to "thorough fermentation" (тщательная ферментация), that is, trying not to overdo it.

Процесс ферментации, проходящий плавно и постепенно, без пиков и спадов.