Context. Shock waves driven by fast and wide coronal mass ejections (CMEs) are considered to be very efficient particle accelerators and are involved in the production of solar energetic particle (SEP) events. These events cause space weather phenomena by disturbing the near-Earth radiation environment. In past studies, we analysed statistically the relation between the maximum intensity of energetic electrons and protons and the properties of coronal shocks inferred at the point of magnetic connectivity. The present study focuses on a gradual SEP event measured by STEREO-A and -B on 11 October 2013. This event had the interesting properties that it (1) occurred in isolation with very low background particle intensities measured before the event, (2) was associated with a clear onset of SEPs measured in situ allowing detailed timing analyses, and (3) was associated with a fast CME event that was magnetically connected with STEREO-A and -B. These three properties allowed us to investigate at a high cadence the temporal connection between the rapidly evolving shock properties and the SEPs measured in situ.Aims. The aim of the present study is to investigate the relative roles of fundamental shock parameters such as the compression ratio, Mach number and geometry, in the intensity and composition of the associated SEP event measured in situ.Methods. We used shock reconstruction techniques and multi-viewpoint imaging data obtained by the STEREO-A and -B, SOHO, and SDO spacecraft to determine the kinematic evolution of the expanding shock wave. We then exploited 3D magneto-hydrodynamic modelling to model the geometry and Mach number of the shock wave along an ensemble of magnetic field lines connected to STEREO-A and -B, also estimating the uncertainties of the shock parameters. Using a velocity dispersion analysis of the available SEP data we time-shifted the SEP time series and analysed the relations between observed SEP properties and the modelled shock properties. We also studied the energy dependence of these relations.Results. We find a very good temporal agreement between the formation of the modelled shock wave and the estimated release times for both electrons and protons. The simultaneous release of protons and electrons suggests a common acceleration process. This early phase is marked at both STEREOs by elevated electron-to-proton ratios that coincide with the highly quasi-perpendicular phase of the shock. These findings suggest that the rapid evolution of the shock as it transits from the low to the high corona modifies the conditions under which particles are accelerated. We discuss these findings in terms of basic geometry and acceleration processes.