When talking about Character Sets in Apache Tika, you need to consider two kinds of files differently. One kind is that of basically just plain text, the other are more complex types (including binary ones)
With the more complex files, Tika mostly uses third party libraries, and these libraries are responsible for returning Java Strings. The exact way of doing that will depend on the file format in question - sometimes the file format will including encoding information, other times it'll be fixed in what it supports. Either way, Tika gets Java Strings, and returns to you a Java String. How you choose to encode that for output is up to you. (For Windows users especially, check the encoding of your terminal, and the font used. There've been lots of "Tika Encoding Problems" which were actually people failing to correctly set the default Java encoding on output, or failing to have a Unicode capable terminal!)
With plain text files, there's no encoding information in the file, all we have is a bunch of bytes. Here, Apache Tika uses one of a number of EncodingDetector instances to do the detection. These use hints, n-grams, language detection etc, to try to work out the most likely encoding of the file based on information given, pattern of bytes in the file etc.
The definition of EncodingDetector is held in the Tika-Core jar, but most of the implentations are held in the Tika-Parsers jar (and loaded by the service loader method, just like Detectors and Parsers). The main ones are here in SVN. If you check there, you'll see the main list of encodings that Tika can detect.
One final thing - the encoding detection is only performed on files that are text files, it isn't done on the binary type files. Depending on how you call Tika, you might need to tweak that and/or provide a hint that it's a text file, so that the EncodingDetector logic gets triggered.