Maximum audio level that can be obtained with digital media is 0dbfs (full scale) anything less than maximum is expressed as a negative number of db.
The specifications they have given you are a hangover from tape delivery days but a lot of cable stations use these specs.
Reference tone. At the start of the program is usually a 30 second or so (the actual length and timecode position of these is often part of the spec.) section of bars and tone. Premiere can generate these bars and you have a choice of SD or HD type. The tone that Premiere generates is at -12db so you will need to change its gain by -8db to make it -20, right click- Audio gain- Adjust gain by -8.
Peak program levels. This is a hangover from analogue tape days where the mod could not go above -10db (maximum level on a PPM meter) If you put a limiter in the master in the track mixer and set it to -5db this should be about right.
Program peaks. This is asking for the average program level to be about the same level as the tone. This has now (in Premiere CC) been replaced by loudness metering. Set the loudness monitor to -23db and play the whole program, this should be within a db or so of -23. Adjust the levels to make it correct.
Having said all this, you were delivering a file based program on dvd, it's just the delivery media you are changing. If they accepted the dvd sound they should have no problem with the file bases alternative.
Others were quicker at typing than me.