Can you explain what an offset parameter is?
In addition to what 'torger' said, successful stitching depends on images that are geometrical distortion free. Even most regular lenses exhibit a certain degree of decentering, and in a T/S lens it is promoted to a feature. So, in order to remove symmetrical pincushion/barrel distortion, the images need to be corrected to images that are perfectly centered before they are corrected for symmetrical/geometrical distortion. That is what the offset parameters (historically parameters 'd' and '' e') are for. Software such as PTassembler, PTGUI, and Hugin, all support those parameters.
Even for non-T/S lenses it can improve the stitching quality if (after regular control point optimization) an intermediate run of only these 2 parameters is done. The reason why these parameters are not routinely included in an optimization run is that it increases the number of variables and thus the complexity and the need for more controlpoints in the overlap region. For lenses that have a serious amount of shift applied (and Tilt usually also introduces a small amount of decentering), the added complexity of the optimal solution will often make a regular stitch impossible, or suboptimal at best.
In my experience, it works best for shifted images when you make a note of the amount of shift that was used, and immediately set that as a starting position for the lens. If you e.g. used 5mm vertical shift on a 24mm high sensor, then you already know exactly how many pixels (usually minus) offset you need to use (5/24 x # of vertical pixels), and it is better to input that manually rather than frustrate the optimization routine by having to search for it. Small amounts of decentering (such as introduced by tilting) can usually be found by using the optimizer, but for larger amounts it helps to get the required amount in the ballpark which will allow the optimizer to converge to an optimum solution faster, instead of getting stuck in another suboptimal local minimum of the solution.
Cheers,
Bart