Reduced duration and damage over time

I had a set up a while ago where i was using caustic arrow with reduced duration support. My logic was that I was doing the same ammount of damage, but faster (+the extra dmg). Enemies and bosses would melt on contact with my caustic spots before I stoped playing, so I don't know if it was the other support gems and gear that was doing the killing or if it was an actual mechanic I was using.

In short, I thought I was dealing 100 dmg over 5 seconds instead of dealing 100 damage over 10 seconds. So dealing 20dmg/sec instead of 10dmg/sec (fictional numbers)

But I don't know if that's the case or not. Just spent an hour on google reading a bunch of topics and none of them seemed to be asking what I'm asking, they all wanted to know stuff about more duration and igniting or whatever.

I'm still early in my leveling and I want to know if it actually does work like that or if i was just getting it wrong so I don't commit to reducing durration again by ignorance.

That's not how it works. Modifying the duration of a damage-dealing effect doesn't inherently increase the damage it deals per second. Less Duration Support applies a more damage modifier, but that's separate from the less duration modifier, which itself only reduces the duration of caustic ground without increasing its DPS. If you attack often enough that there's always caustic ground under the monster, this might not have any practical effect. There are modifiers that say something like "Ailments deal damage x% faster", which does increase their DPS, but to my knowledge they don't apply to non-Ailment DoTs.