This gives you the average image (intensity or FODs) of the rigidly aligned images. Registration is performed iteratively in a pairwise manner between each subject image and the current best estimate of the template. After each stage, the template is updated with the average of the rigidly transformed images (see diagram here). This is what happens behind the scenes in population_template, nothing you need to worry about.
The template is the unweighted average intensity of all images (time points) mapped to the common space via subject to template transformations. In your case, the template works as mid-point so you’d transform each image to the subject-specific template space. You can use population_tempalte with rigid, affine or nonlinear registration to create this central reference space.
Note that there are other registration approaches to align multiple images to a common central point (based on (pairwise) distances in deformation space for instance) but not within MRtrix. For more information on the topic see for instance The optimal template effect in hippocampus studies of diseased populations, Avants et al.. If you wanted to adjust the “centre” point of the subject-specific template, you’d need to get your hands dirty as the MRtrix tools were not designed for this. I guess the easiest would be to adjust population_template to perform a weighted intensity average based on temporal distance from the target time point. This would bias the template’s representation towards the target time point’s representation and therefore nudge registration towards that time point’s shape as well. It is probably not the best™ approach from a theoretical point of view but I’d guess it would work reasonably well in the absence of large deformations between time-steps.