This guide is primarily concerned with P-TTL operation. However, older camera bodies do not support this, and it is sometimes desirable to have the flash choose the appropriate power level itself.
P-TTL works by sending a small flash pulse at much less than full power. Light bounced back to the camera from this preflash is used to compute the amount of power required for the real flash, which follows nearly instantaneously. Old-style TTL worked by measuring light reflected off of the film, or from the sensor in early Pentax models. Apparently this was problematic when used with modern sensor coatings, so this mode is no longer available in current camera bodies — a discussion for another article.
The Pentax, Metz, and Sigma models all automatically revert to regular TTL on camera bodies where that is available but P-TTL is not. The Promaster flashes don't support regular TTL and will fire at full power. It is unclear how Tumax/generic flashes behave in this situation and it may depend on the specific version. (And some older versions of the generic flashes only support old-style TTL.)
It's important to keep in mind that this is strictly a backwards-compatibility feature. The old-style TTL requires an additional light sensor in the camera body, and that's unlikely to come back.
It would sometimes be convenient for the flash to be able to choose the appropriate power level automatically itself. P-TTL isn't available with manual-focus lenses which lack electronic communication with the camera body, and it handles some scenes (particularly when there are reflective surfaces in the shot) erratically.
This is sometimes called "auto thyristor", and requires a sensor on the flash, which most models do not have — only the Pentax AF360FGZ and AF540FGZ, and the Metz 58 AF-1/AF-2. The Metz 54 MZ-4i has an auto sensor in the Pentax-specific module and can also use the auto-only standard SCA 301 module.
Auto mode on the Pentax flashes is clearly intended for older camera bodies. Zoom information isn't automatically communicated and must be set manually. Also, many people find it annoying that the flash will reset to P-TTL mode whenever resuming from auto-off (while the Metz 58 AF-1/AF-2 stays where you left it).
Somewhat oddly, when a Pentax flash is in auto mode and the camera is in P or Tv (shutter priority) mode, the camera gets (and sets itself to) the appropriate aperture based on directions from the flash. (Including automatically doing the right thing for different ISO settings.) The Metz 58 AF-1/AF-2, by contrast, works the other way around: the flash automatically reads the current aperture and ISO information from the camera (which works in all program modes).
Promaster offers a separate module (the FTA5000) for its 5000-series flashes which makes them work in auto mode.