Independent vector analysis (IVA) and tensor decomposition are two types of effective algorithms for joint blind source separation (JBSS) with different statistical assumptions. Although IVA and tensor decomposition are intrinsically linked, their explicit connection has not been reported. In this letter, we reveal their explicit connection through a piecewise stationary multivariate complex Gaussian signal model. With this model, IVA can be explained as reconstructing the covariances of the mixtures in a similar manner as double coupled canonical polyadic decomposition (DC-CPD), a typical tensor-based algorithm, with the only difference being the distance metric used in the cost function. Numerical experiments show that IVA can achieve better separation performance but is highly dependent on how well the a priori model matches the actual signal, while DC-CPD is more robust to the model mismatch.