Slice timing correction is done to correct for the order of the slice acquisition. If the volume has been rotated for motion correction first, this timing information will be practically useless, particularly for alternating slice order (interleaved) acquisition and the various interpolation methods. If motion is anywhere near half a voxel or more in the slice dimension, that makes slice timing correction less valid. The bookkeeping of finding original timing information for each voxel rather than each slice becomes much more complicated and is not done in our software either (for both 3dTshift and 3dvolreg -tshift). Of course, slice timing correction does not necessarily need to be done at all, and that can depend on how accurate stimulus timing needs to be for your particular experiment, and that may depend in turn on the kinds of stimuli and response and the response functions used in your model.

In AFNI, afni_proc.py uses the slice timing correction and then motion correction as its default, but you can modify the order if you want. In align_epi_anat.py,, the same order is used, but can not be modified. align_epi_anat.py is used principally to align epi and anat data, not to do preprocessing for analysis, so you need not use the slice timing corrected data at all. For both these scripts, slice timing correction and motion correction are optional.

A previous message board posting addressed this issue in combination with yet a third element of correcting for respiration and cardiac cycle.

[afni.nimh.nih.gov]

I believe in FSL, there is a program that attempts to resolve both motion correction and slice timing correction at the same time, but I haven't tried their program.

[www.fmrib.ox.ac.uk]

A quick literature search found these papers. The first one is a study (Tyler Jones, Rasmus Birn and Peter Bandettini who are all at NIH here) in combination with respiration, cardiac cycle correction, but looked closely at the order of operations.

[dx.doi.org]
[dx.doi.org]

[books.google.com]

In the end, whether to do slice timing correction and order will be it depends.... But you can always try several ways to see what makes sense for your data.