Integrating floating offshore wind turbines with oscillating-water-column wave energy converters has been seen as a promising solution for hybrid offshore renewable energy production, as the cost-effective wave energy devices could possibly help increase the overall power absorption, reduce platform dynamic responses, and mitigate loads for critical wind turbine structures etc. As most existing research works on dynamic analysis of these hybrid concepts are based on frequency-domain simulations or scale model experiments, this work focuses on establishing an aero-hydro-elastic-servo-mooring coupled numerical framework for integrated time-domain dynamic analysis. In particular, the water column dynamics are characterised based on an equivalent virtual oscillating body approach so that the time-domain analysis capability for oscillating-water-columns with power take-off control is enabled. For validation, a novel combined concept is designed, and its time-domain numerical results under various environmental conditions have been compared against the 1:50 scale model wave basin test data. Good agreement has been observed between the numerical and experimental results, demonstrating the feasibility of the proposed numerical framework. Furthermore, different power take-off control strategies for the oscillating-water-column wave energy converters have been proposed, and it is found that the designed gain-scheduling control schemes are more beneficial for mitigating the platform motion responses and wind turbine structural loads compared with traditional linear damping control, resulting in 15% platform pitch motion mitigation and 6% tower base fatigue load reduction. Further studies on multi-objective optimal power take-off control design regarding both load reduction and power maximisation could be conducted for hybrid energy platforms based on the established numerical framework.