The past tense focuses on a completed action:
聞いたそばから忘れてしまう - As soon as I've heard something, I forget it.
読んだそばから抜いていって何も覚えていない - As soon as I've read something, I don't remember what it was about.
Present tense focuses on a habitual pattern:
子供は作るそばから食べてしまうので、作っても作っても追いつかない - As soon as I make something, my kids eat it so even if I cook and cook there's no keeping up.
我が家もそうなのだけれど、片付けるそばから散らかすし拭いたそばからこぼされる。 Our house is like this: as soon as we clean up, it's messy; as soon as we wipe something up, something spills. (on going struggle)
片付けるそばから散らかす - as soon as we clean it, it gets messy (on going)
片付けたそばから散らかす - as soon as I've cleaned it, it gets messy (on going, but sounds more punctuated)
片付けてるそばから散らかす - doesn't work because TE-IRU persists for a span of time. This verb type would "be as soon as we're cleaning it."