It is significant to employ multiple autonomous underwater vehicles (AUVs) to execute the underwater target tracking task collaboratively. However, it's pretty challenging to meet various prerequisites utilizing traditional control methods. Therefore, we propose an effective two-stage learning from demonstrations training framework, FISHER, to highlight the adaptability of reinforcement learning (RL) methods in the multi-AUV underwater target tracking task, while addressing its limitations such as extensive requirements for environmental interactions and the challenges in designing reward functions. The first stage utilizes imitation learning (IL) to realize policy improvement and generate offline datasets. To be specific, we introduce multi-agent discriminator-actor-critic based on improvements of the generative adversarial IL algorithm and multi-agent IL optimization objective derived from the Nash equilibrium condition. Then in the second stage, we develop multi-agent independent generalized decision transformer, which analyzes the latent representation to match the future states of high-quality samples rather than reward function, attaining further enhanced policies capable of handling various scenarios. Besides, we propose a simulation to simulation demonstration generation procedure to facilitate the generation of expert demonstrations in underwater environments, which capitalizes on traditional control methods and can easily accomplish the domain transfer to obtain demonstrations. Extensive simulation experiments from multiple scenarios showcase that FISHER possesses strong stability, multi-task performance and capability of generalization.