In this paper, we consider the generalized coupled Sylvester tensor equations by the tensor forms of the biconjugate A-orthogonal residual and the conjugate A-orthogonal residual squared algorithms. With the absence of round-off errors, we show that our methods converge to the exact solution group within finite steps when they are consistent. Finally, we provide some numerical examples to demonstrate the effectiveness of the proposed methods, including when testing the algorithms by color image restoration problems and randomly generated data.