Industry 4.0 comes with the human-autonomy teaming (HAT) paradigm. Autonomous agents and operators are working as teammates with complementary competencies. Agents can make proposals thanks to new sensor technologies and data analyzing methods. The operator’s new task is to accept or reject these proposals. Consequently, trust is central in an HAT environment. This experiment aims to understand the effects of agent-generated information on the operators’ decision-making, trust, and risk perception during cooperation operations. This cooperation aims to help operators to manage maintenance dates in a maritime context. To this end, participants formed a team with a predictive maintenance system that provided them with proposals for modifying the schedule. In each situation, participants had to decide whether to comply with the proposal or not. The variables modified were agent transparency (transparency about analytical uncertainty and/or environmental projections) and situation criticality (moderate or high). The participants’ trust, risk perception, and compliance were measured. The results show that trust is a predictor of decision-making and risk perception is a moderator of trust. Transparency and situation criticality, and their interaction, influence participants’ trust and risk perception. These effects are also present in participants’ compliance. Notably, transparency in the environmental projections with a high-criticality situation leads to lower compliance. Agent transparency and situation criticality play an important role in operator decision-making and trust building. As transparency helps improve HAT, situation criticality must be taken into account for a better understanding of its effects.