In this paper, we investigate the semi-tied Gaussian mixture models for robust learning and adaptation of robot manipulation tasks. We make use of the spatial and temporal correlation in the data by tying the covariance matrices of the mixture model with common synergistic directions/basis vectors, instead of estimating full covariance matrices for each cluster in the mixture. This allows the reuse of the discovered synergies in different parts of the task having similar coordination patterns. We extend the approach to task-parameterized and hidden semi-Markov models for autonomous adaptation to changing environmental situations. The planned movement sequence from the model is smoothly followed with a finite horizon linear quadratic tracking controller. Experiments to encode whole body motion data in simulation, followed by valve opening and pick-and-place via obstacle avoidance tasks with the Baxter robot, show improvement over standard Gaussian mixture models with much less parameters and better generalization ability.