Marco never says this.
The line you are referring to is "Nothing happened. It's like our souls are bonded-"
However, this is not Marco explaining what's actually happening. This is Marco trying to explain why the wand didn't transform when he initially touched it. The fact that the wand transforms immediately afterwards makes the statement meaningless, because what he thought was happening wasn't actually happening.
Furthermore, magic in SVTFOE has nothing to do with souls. It has to do with physically tapping into the realm of magic to create some sort of desired effect.
In fact, we have actually seen magic being channeled from one person to another in "Moon the Undaunted" when Moon uses the darkest spell. Both her and Eclipsa's cheekmarks glow when the spell is used. When Marco uses the all-seeing eye, Star's cheekmarks do not glow.
The blood moon explanation is honestly the least-sensible theory there is if you take the starco goggles off.