Hood was briefed on the mission details by Chen Yu before she arrived, and even the four young girls of the 6th Destroyer Squadron were aware of their roles, which is why Akatsuki was unwilling to play earlier.
However, according to Chen Yu's plan, all they needed to do was pretend to encounter each other by chance, then let the 6th Destroyer Squadron innocently provoke the situation. Meanwhile, Chen Yu would secretly influence the emotions of the two individuals, causing a shift in their feelings for each other and thus bridging the gap from would-be lovers to an actual couple.
The relationship between Tokairin Yūko and Inomata Naoki was crucial to the progress of the entire plan. With the Red String of Fate around Minami already showing signs of change, Chen Yu couldn't afford to let their relationship develop at its own slow pace. If it took these two slow-warmers several months without progress, while Minami grew fond of Inomata Naoki, that could disrupt Chen Yu's master plan.