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New evidence based on Cassini magnetic field and plasma data has revealed that the discovery of Titan outside Saturn's magnetosphere during the T96 flyby on 2013 December 1 was the result of the impact of two consecutive interplanetary coronal mass ejections (ICMEs) that left the Sun in 2013 early November and interacted with the moon and the planet. We study the dynamic evolution of Saturn's magnetopause and bow shock, which evidences a magnetospheric compression from late November 28 to December 4 (at least), under prevailing solar wind dynamic pressures of 0.16-0.3 nPa. During this interval, transient disturbances associated with the two ICMEs are observed, allowing for the identification of their magnetic structures. By analyzing the magnetic field direction, and the pressure balance in Titan's induced magnetosphere, we show that Cassini finds Saturn's moon embedded in the second ICME after being swept by its interplanetary shock and amid a shower of solar energetic particles that may have caused dramatic changes in the moon's lower ionosphere. Analyzing a list of Saturn's bow shock crossings during 2004-2016, we find that the magnetospheric compression needed for Titan to be in the supersonic solar wind can be generally associated with the presence of an ICME or a corotating interaction region. This leads to the conclusion that Titan would rarely face the pristine solar wind, but would rather interact with transient solar structures under extreme space weather conditions.