You control the last ability of Deadly Designs, no matter who activated the ability to give it its fifth plot counter.

You must sacrifice Deadly Designs as its last ability resolves. However, you can choose zero creatures as targets if you want.

If the player who controlled Deadly Designs as its last ability triggered doesn't control it as that ability resolves, Deadly Designs won't be sacrificed. The same is true if each of the ability's targets are all illegal by the time the ability resolves. However, if it's still on the battlefield and has five or more plot counters on it, its last ability will immediately trigger again.