You need to rembember that you (as well as me) are living in a moderate climate with probably not a lot of high temperature days, but if you live at a place where it's constantly 30C, the temperature of you tank will rise as well. Axies don't do well in high temperatures, but dwell well in the lower ones. I'm not an expert, but what I know is that higher temps will kill an axie, lower ones will slow it down (also it's metabolism). I even read about people that kept their axies in the pond for a period and the top of it froze, and the axies were still fine.
Those bottles of ice are meant to cool the water, but you are right about big temp changes, so people shouldn't do this without thinking about how to maintain the cooler temperature.