The fictitious force changes sign depending upon which of ω I and ω S is greater. The reason for the sign change is that when ω I > ω S, the spheres actually are moving faster than the rotating observers measure, so they measure a tension in the string that actually is larger than they expect; hence, the fictitious force must increase the tension (point outward). When ω I < ω S, things are reversed so the fictitious force has to decrease the tension, and therefore has the opposite sign (points inward).