The 3D camera tracker sets a camera focal length and animates it's path. Your assumption that this data should be applied to an obj imported into AE is incorrect. The workflow would be to save your 3Ds Max model as an obj file and import that into C4D lite or Element 3D to let AE's camera interact with the model or to export AE's camera data to 3Ds Max and render an image sequence to be used as a footage layer.
Could you suggest me the right way to link 3D model to the footage? Maybe i should be oriented in C4D or other software instead AE?