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Given the rapid rise of electric vehicles (EVs) worldwide, and the ambitious targets set for the near future, the management of large EV fleets must be seen as a priority. Specifically, we study a scenario where EV charging is managed through self-interested EV aggregators who compete in the day-ahead market in order to purchase the electricity needed to meet their clients' requirements. With the aim of reducing electricity costs and lowering the impact on electricity markets, a centralised bidding coordination framework has been proposed in the literature employing a coordinator. In order to improve privacy and limit the need for the coordinator, we propose a reformulation of the coordination framework as a decentralised algorithm, employing the Alternating Direction Method of Multipliers (ADMM). However, given the self-interested nature of the aggregators, they can deviate from the algorithm in order to reduce their energy costs. Hence, we study the strategic manipulation of the ADMM algorithm and, in doing so, describe and analyse different possible attack vectors and propose a mathematical framework to quantify and detect manipulation. Importantly, this detection framework is not limited to the considered EV scenario and can be applied to general ADMM algorithms. Finally, we test the proposed decentralised coordination and manipulation detection algorithms in realistic scenarios using real market and driver data from Spain. Our empirical results show that the decentralised algorithm's convergence to the optimal solution can be effectively disrupted by manipulative attacks achieving convergence to a different non-optimal solution which benefits the attacker. With respect to the detection algorithm, results indicate that it achieves very high accuracies and significantly outperforms a naive benchmark.