Serum before or after moisturiser?

I just bought a serum, which I have never really used in my routine. I cleanse, exfoliate, tone, apply eye creams, and moisturize in the PM. The bottle of my serum says to apply it to my face, neck, and décolletage before a moisturizer. That doesn’t seem right to me after all the routine searching I’ve been doing. Help or advice, please?

I’ve got the Thursday Plantation Tea Tree oil moisturiser and the serum is Sukin Super Greens Facial recovery serum.

I have a similar routine and I use the products in this order: cleanse, exfoliate, tone, serum, and then eye creams/ moisturize.

Oil cleansers —> Aqueous Cleansers —> Toners —> Serums —> Emulsions —> Moisturizers —> Oils —> Occlusives

Where exfoliation falls depends on the type of exfoliator and the pH