I get the feeling the transient solver in HFSS is a bit of an after-thought, most probaby added just so Ansys can say it has the features of other software such as EMPro which uses FDTD. There does not seem to be much information on it. Although the manual covers the transient solver, the manual has not been updated since version 11. There are to my knowledge no application notes or tutorials specific to the transient solver.
I've been on a couple of HFSS courses (one basic, one advanced), as well as an HFSS Antennas Workshop. All these were presented by Ansys, but not once was the time-domain solver covered.
Perhaps others feel differently, but I don't think the transient solver gets much attention.
Dave