So first, your warlord should be someone with General Tax [Zhuge Liang (Sage), Tian Feng, or Xu Shu]. They have the best warlord ability that gives the biggest bonus to your resource production.

But here's the important part, activating your ability doesn't actually just increase your production by the amount stated. It actually increases the amount of resources currently in storage waiting to be collected as well. It also decreases your stored taxes at the end of the ability cooldown. So you only want to use it right before you collect, and you only want to collect while it is active.

Otherwise you're likely wasting your ability, like I have been for the past month. Cheers.

edit: Slight change, Here's an in-depth video demonstrating the issue