With the camera on Auto the OM-4Ti (and the OM-2, OM-2n, OM-2SP, OM-4)will all give TTL automatic exposure with the T32. The viewfinder light will flicker because there is a dedicated third contact on the hotshoe that allows exposure confirmation display to be shown. If the light on the back of the flash flickers but the one in the camera doesn't then it sounds like yours isn't working correctly. Mention it when you send the camera in for CLA.
The shutter speed setting is irrelevant when the camera is in Auto mode. Use the 60 (1/60th second) if you switch to manual.
With the calculator panel showing you have the options:
Manual, full power (GN 32 metres)
Manual, half power (GN 16 metres)
3 Normal Auto settings with appropriate max distance for each. These work like an offbrand auto flash unit and use the sensor inside the 'O' on the front (so don't go covering it up) instead of inside the camera.
There are specifications and a PDF of the T32 instruction manual at the bottom of
http://olympus.dementia.org/eSIF/om-sif/flashphotogroup/t32.htm which should explain it better (there are specifications and manuals for most OM components there, in fact).
A comprehensive Olympus OM FAQ that answers lots of other questions about Olympus cameras and lenses is at
http://brashear.phys.appstate.edu/lhawkins/photo/photo.shtml
Simon.