If the station is broadcast with it's callsign in the digital stream it's presented in the 'tuner callsign' field. In my experience a lot (especially on Cable) of stations are not broadcasting their callsigns (there's no requirement to do this on Cable). Over the air stations generally do broadcast their callsigns (I believe it's an FCC requirement) and many cable companies propagate that information into their systems too (though some do not).
However there's very little consistency between the callsign that is broadcast and the callsign thats present in the listings. iOnTV attempts to make a match if it can (and the matching logic needs improvement) but often it can't and it's up to you to make the matches manually. You don't actually need to edit the tuner callsign to do this - just associating a listing callsign with the specific channel.program will do.
iOnTV needs the match so that when you choose a program to record from the schedule grid it can track the program back to a tuned channel to record it. If you see the 'watch', 'record' etc items being grayed out for all programs on a given channel then that's because that channel hasn't been matched up in the channels pane of the preferences on any tuner.