Yes, that certainly could explain it. As it says on both the product pages and in the documentation, Octolively requires a _regulated_ 5V power supply. A regulated power supply typically keeps the output voltage within about 1% of the nominal value. An unregulated power supply like the one that you have may give 6 V before being plugged in, but may droop as low as 3 V once under power. This is not a safe or reliable way to drive these modules.
A value greater than 5.5 V can potentially (but does not usually– these are tough chips) permanently destroy the AVR microcontroller. It is also possible that the program was corrupted due to some unfortunate timing coincidence of the power dropout.
You could certainly attempt to reflash the chips, or you could send them back to us for reflashing (no cost except postage), or order a set of pre-flashed replacement chips.
If you’d like to reflash them yourself, you’ll need an AVR ISP programmer, or you can substitute (for example) an Arduino, using the ArduinoISP method. The source code is available here: https://github.com/evil-mad/Octolively