We investigate the effect of exit pressure history on the flow characteristics of underexpanded transient jets. Using both experiments and numerical simulations, we study the dynamics of shock-cell and vortex structures within these jets. A shock tube with an open-ended configuration allows us to generate transient jets by adjusting the diaphragm pressure ratio and the length of the driver section. Our results indicate that when the shock Mach number exceeds 1.6, a Mach disk forms, indicating a highly underexpanded transient jet at the exit of the shock tube. A distinguishing feature of this jet is the emergence of counter-rotating vortex rings (CRVRs) alongside the initial primary vortex ring. Our findings reveal a substantial influence of both the amplitude and duration of the peak exit pressure on the characteristics of the Mach disk and vortex ring. Notably, the characteristics of the primary vortex ring exhibit significant sensitivity to the formation and evolution of CRVRs. In cases of continuously decreasing exit pressure, the Mach disk follows a consistent self-similar decay pattern, regardless of the peak exit pressure magnitude. Finally, we present an empirical relationship between exit pressure and the characteristics of the Mach disk. In summary, this research provides insight into the complex interaction between the exit pressure history and the flow characteristics in underexpanded transient jets.