The Minty will handle input voltages down in the 2.5v range - with decreased efficiency. The real question is what was the voltage output of those cells when they were still under load. Given the heating, I'm pretty certain it was lower than 1.2v.
For modern smart-phones with their high-capacity batteries, I like the 3x NiMH cell configuration. The 3.6v output is right in the MintyBoost's efficiency sweet-spot, and the cells hold up much better than alkaline cells in high-drain applications. If you do stick with Alkaline, look for cells designed for high-drain usage. Check here for more details: viewtopic.php?f=15&t=22377