This ImageJ plugin is for applying 2D slice alignment to all slices in a 3D+t hyperstack.
ImageJ/Fiji and Template Matching and Slice Alignment --- ImageJ Plugins
Copy a plugin file align_slices3d-1.0.0.jar to the plugins/ directory of your ImageJ/Fiji.
First, prepare a 2D+t stack from your 3D+t hyperstack (e.g. maximum projection, specifying a Z level).
Run Plugins>Template Matching>Align slices in stack... as instructed here with the "show align coordinates in results tabl" option.
Open the 3D+t hyperstack and run Plugins>Hyperstack Slice Alignment.