Sounds like you didn’t actually manage to use up enough battery to drop down to Mountain Mode. If you switched your 2013 Volt from Hold into MM with more than ~4 bars of power remaining, you were driving up that hill in Electric Mode.Found another part of the manual with more info on the modes.
Tried Mountain Mode today on a long steep grade. I had been on hold mode saving my battery and I went to MM and it just went up the hill on the battery, never started the ICE.
It doesn't have any problem on battery, I like to use hold but it feels under powered sometimes.
When you switch a Gen 1 Volt into MM with more than ~4 bars of power still in the battery (~2 bars for Gen 2), you continue driving in Electric Mode on battery power until the battery’s charge has dropped to that ~4 bar level. At that point, the ICE starts, and it’s just like you’re driving in Hold Mode.
You can test this out any time... when you switch a 2011/2012 Volt into MM, the ev range immediately drops by ~14 ev miles (the MM buffer). Later mode Volts "gray out" the bottom battery bars. If you then still have green bars remaining, you continue driving on grid battery power (2011/2012 owners continue until the new range estimate drops to 0). Switching back to Normal will make that reserved power available again.
If you switch after you drop below that 4-bar (or 2-bar) level, or wait until the battery is fully depleted, MM includes a "feature" that recharges the battery to the 4-bar (2-bar) level as you drive, burning a little more gas for this purpose. This allows you to recharge that buffer without having to stop and plug in to the grid before heading into the mountains. (If you later switch back to Normal, you drive Gas Miles on this battery-power-created-by-burning-gas until it’s used, then the car switches back to green bars of grid power.)
The Self Charging Chevy Volt youtube video shows a 2012 Volt with a fully depleted battery being recharged via MM. The procedure takes 15 minutes, and uses 0.36 gallons of gas. The video shows this happening while the Volt is parked, but I’ve seen no reports that suggest the process takes any longer or uses any more gas if done while driving along in moderate conditions. That’s why the manual tells you to switch to MM about 15-20 minutes before heading into the mountains.