As already mentioned, processing just produces a developed negative. A 'professional' telecine will be able to take the negative and produce a correct positive version on video, it will also be able to alter the contrast/colour balance etc. at the same time. Be aware of the differences between a "One Light", and a "Best Light" Tk.
I haven't had any dealings with "DigitalCopyCat", but you need to be wary of places that appear to specialise in 'telecine' of home movies to DVD/MiniDV. A lot of these companies will use equipment that varies from a projector and video camera, up to dedicated transfer machines (some of which offering very good results) - but most will be optimised for transferring positive reversal film, and almost all will fail to handle negative film properly, if at all.
As a generalisation, most of the labs able to process 16mm negative film will be able to properly telecine it as well. If you're a film student most labs will be able to offer discounted rates. Personally I've only used Todd-AO (now merged into part of "Soho Film Lab"), and "Technicolor Creative Services". Both have been most helpful and happy to tell me their rates and minimum charges. Feel free to check prices with a number of different labs and check what that price includes - the amount varies quite a bit for similar services, and when you're paying from your own pocket on limited funds it pays to double check first!