AI has revolutionised decision-making across various fields. Yet human judgement remains paramount for high-stakes decision-making. This has fueled explorations of collaborative decision-making between humans and AI systems, aiming to leverage the strengths of both. To explore this dynamic, researchers conduct empirical studies, investigating how humans use AI assistance for decision-making and how this collaboration impacts results. A critical aspect of conducting these studies is the role of participants, often recruited through crowdsourcing platforms. The validity of these studies hinges on the behaviours of the participants, hence effective incentives that can potentially affect these behaviours are a key part of designing and executing these studies. In this work, we aim to address the critical role of incentive design for conducting empirical human-AI decision-making studies, focusing on understanding, designing, and documenting incentive schemes. Through a thematic review of existing research, we explored the current practices, challenges, and opportunities associated with incentive design for human-AI decision-making empirical studies. We identified recurring patterns, or themes, such as what comprises the components of an incentive scheme, how incentive schemes are manipulated by researchers, and the impact they can have on research outcomes. Leveraging the acquired understanding, we curated a set of guidelines to aid researchers in designing effective incentive schemes for their studies, called the Incentive-Tuning Framework, outlining how researchers can undertake, reflect on, and document the incentive design process. By advocating for a standardised yet flexible approach to incentive design and contributing valuable insights along with practical tools, we hope to pave the way for more reliable and generalizable knowledge in the field of human-AI decision-making.