The China Space Station Telescope (CSST) is a 2 m three-mirror anastigmat equipped with a Fast Steering Mirror (FSM), which is part of its precision image stabilization system. The FSM is used to compensate for residuals from the previous stage of the image stabilization system. However, a new type of image stabilization residual caused by image rotation and projection distortion is introduced when the FSM performs tip-tilt adjustments, reducing both the image stabilization accuracy and the absolute pointing accuracy of the CSST. In this paper, we propose a scheme to compute the image stabilization residuals across the full field of view (FOV) by using a reference star as the target for stabilization control, which can be utilized for subsequent image position correction. To achieve this, we developed a linear optical model for image point displacement by simplifying an existing image point displacement model and incorporating more readily available parameters. The computational accuracy of the new model is equivalent to that of the original, with computational differences of less than 0.03 μm. Based on this linear model, we established a calculation model for image stabilization residuals, including those due to image rotation and projection distortion caused by FSM tip-tilt adjustments. This model provides a theoretical foundation for quantifying such residuals during the image stabilization process. Finally, the results of testing using this scheme are provided. Experimental results demonstrate that within the observation FOV of the CSST, when the FSM tilts by (1'', 1''), the maximum absolute value of the image stabilization residuals accounts for 20% of the total image stabilization accuracy requirement. This finding underscores the necessity of computing and correcting these residuals to meet performance requirements.