3drefit only affects the .HEAD file -- you are just telling AFNI what way the data is oriented as it is stored in the .BRIK file. If some of your datasets are actually stored in RAI orientation, say, and some in LAI, then you cannot flip the RAI ones to LAI just by using 3drefit -orient.
3dDeconvolve (or 3dTcat) simply catenates the datasets in time, VOXEL BY VOXEL. The output will have the same physical orientation, grid spacing, et cetera, as the first input. If in fact some of your input datasets are not stored in the same orientation, you will not get correct results from the program -- it does not attempt to flip input datasets to match one another.
If you want to physically flip a dataset to a different orientation, the 3dresample program can be used.