Are you referring to this description? * Double the duration of Health Regeneration, Damage Buff, and Power Free casting for yourself. (Unique to your own Supply Drop)
The philosophers stone does not how abilities work. So no it will not buff the duration of neo venom boost. The description you are referring to is the duration of the artifact buffs when you have it normally, for 8 seconds you will have 0 power cost. And you will gain the regular damage buff. When you have it maxed the doubling of buff duration is talking about the supply drop buff. So instead of 8 seconds you will have the amplified supply drop buff for 16 seconds. This means got 16 seconds you will have 0 power cost abilities, health regen, and damage buff.
Wow what a big let down. I thought I could also increase the buff duration for Circuit Breaker using the stone artifact.