Understanding and predicting the behavior of nanomaterials composed of plasmons interacting with quantum emitters at ultrafast timescales is crucial for the better manipulation of light at the nanoscale and advancing technologies like ultrafast communication and computing. Here we perform a simulation of the "real-time" electronic dynamics of a coupled molecule-metal nanoparticle dimer interacting with an ultrashort resonant laser pulse by combining the real-time time-dependent density functional theory (RT-TDDFT) approach with the time-domain frequency-dependent fluctuating charge (TD-ωFQ) model, an atomistic electromagnetic (AEM) model for the dynamic plasmonic response of nanoparticles. It is shown that the induced dipoles evolve from an exponential decay pattern to a beat pattern with an increase in coupling strength, which is altered by changing the molecular orientation relative to the dimer axis. It is further shown that in the strong coupling regime, both the excited molecule and the plasmon relax rapidly due to the molecule-plasmon interaction, and the efficient coherent energy exchange between the interacting molecule and plasmon modes occurs on a femtosecond (fs) timescale. This work provides guidance on manipulating light-matter interaction and studying molecular plasmonics at extremely fast timescales.