Here is presented a fully ab initio theoretical framework for simulating the correlated manyelectron dynamics occuring during and emerging from molecular ionisation by attosecond laser pulses. The method is based on the time-dependent (TD) version of the B-spline restricted correlation space (RCS) algebraic diagrammatic construction (ADC), with the full description of the photoelectron and inclusion of electron correlation effects, such as shakeup processes and interchannel couplings. The nature of the ultrafast charge dynamics in the molecular ion is elucidated by quantitatively predicting the degree of electronic coherence and eigenstate content of the prepared molecular cationic state, beyond the commonly used sudden approximation. The results presented here for the acetylene and ethylene molecules show that even in the high photon energy regime the simulated hole dynamics is quantitatively different from the prediction of the sudden approximation. Moreover, for high-bandwidth ionising pulse the residual interaction between the cation in highly-excited shake-up states and the emitted slow photoelectron gives rise to a loss of coherence in the ionic system which can persist in the first few femtoseconds after ionisation.