HA HA HA HA HA
Sorry. Fire the trainer.
Exercise is typically 8-12 cals per minute, so the 9 you got for 1 minute is pretty accurate. The suggestion that you could burn 30cals per minute (600 in 20 mins) is just absolutely outrageous. So far beyond reality I'm laughing out loud at your trainer.
The thing is though, HIIT, when done properly, elevates your burn after you do it as well, like strength training does. So you won't burn 600 calories in those 20 minutes, but you'll burn more over the next few hours as well as what you burn while doing it.
Best suggestion is to use your HRM and record the 9cal per minute of that, and consider any extra 'afterburn' of HIIT as a bonus that will off-set any errors in calculations. This is why we tend to try to log lower than reality rather than higher for all estimations - so we don't overstate things.
Deb, in New Zealand