Bacteria are, in general, much more capable at processing various chemicals than humans are. They can even pass around packets of genetics, called plasmids, across species. So it isn't really surprising if bacteria can flourish eating something that tastes sweet to people, but doesn't provide any calories to people. There have been some artificial sweeteners shown to hurt bacteria more than people - Xylitol is famously used in gum, for example, because it costs bacteria energy to try to eat it, but they gain nothing, thus helping to fight bacteria growth.
Aspartame is essentially just a collection of amino acids, so it's even more feasible (in a total guessing hand-wavey way) that gut bacteria would be affected.