Tempest and Summons

I'm wondering how Tempests work for players with minions and totems.
Lets say I'm in a map with a rarity or corrupted tempest, and I stand in the tempest. Is that enough to get the bonus on kills, or must my minions also be affected by the tempest?

I'm a bit confused by it on my Raging spitirs character, so I always just waited until the tempest spawned under the mobs before killing them to be sure.

Some clarification would be much appreciated.