This paper studies a same-day crowd-sourced delivery setting where in-store customers deliver online orders on their way home. This environment is dynamic and uncertain, characterized by fluctuating numbers of in-store customers and online orders throughout the day, and unpredictable customer decisions to accept or reject delivery tasks. To address these challenges, we develop a two-stage event-driven dynamic matching framework. The first stage leverages short-term predictions about future arrivals of in-store customers and online orders, allowing us to postpone matching decisions for certain drivers and orders, thus optimizing immediate outcomes to maximize order satisfaction over a future time interval. In response to these initial outcomes, the second stage computes the probability of in-store customers accepting matched orders and introduces two compensation models. These models are designed to tailor compensation for each customer, aiming to minimize expected delivery costs at the current decision-making point. Experimental results demonstrate that our framework reduces delivery costs by approximately 15% compared to baseline methods, highlighting its potential to improve the efficiency of crowd-sourced delivery systems in a constantly changing market.@en