Linger Illusion (Buff) + Persistence (Support Gem) Is Confusing

I am confused by the following result, so posting this question here will hopefully help me find clarity to this concern:

In the Gem-Cutting Menu, why does the Lingering Illusion buff recommend that the Persistence skill gem be used on it, but the Skill Menu Stat Window for the Lingering Illusion skill shows that the "Use Time" of the Illusion is not increased in duration at all?

Isn't the Illusion's "Use Time" duration suppose to increase by 40%?

Is this result a game bug?
Is there a statistic that I am not understanding properly?
Or is this result intentional?

I would love to get feedback on this topic, because this outcome is quite confusing to me.

Thank you.