When neurons activate, they release a neurotransmitter (typically glutamate) that then binds to nearby astrocytes. Astrocytes then increase their intracellular calcium levels which in turn causes vascular dilation of the nearby area, thus increasing blood flow to that area.
I am continually amazed at the level of automated preprocessing tools to deal with this alignment problem. You can play around with fMRI data using some popular packages without thinking too hard about it and produce visualizations almost as nice looking as the ones in the article.
I should add that every full moon a study comes out criticizing fMRI or drawing attention to its limitations, but researchers are very well aware of that. The fMRI response* to a task is neither temporally nor spatially specific, and it is confounded by anything that could remotely influence blood flow and blood volume. Figuring out how to deal with these issues is an active area of research - see an informal discussion here [3].
It's really a shame that the field is purported so negatively by the press, given it's the only thing we have to study brain function in humans with sub-millimeter spatial resolution non-invasively in-vivo.
[1] http://scholarpedia.org/article/Neurovascular_coupling [2] https://www.cell.com/neuron/pdf/S0896-6273(17)30652-9.pdf [3] https://practicalfmri.blogspot.com/2017/08/fluctuations-and-...
* Assuming the conventional Blood Oxygenated Level Dependent contrast used for functional imaging.
Anyway, here's my impression at a high level: neurons need energy to spike, and increased brain activity in a particular brain region ought to translate to higher metabolic activity, and ultimately to higher blood flow (to deliver e.g. oxygen). However, what one can infer about neural activity from e.g. blood oxygen level is still a matter of debate, precisely because (again as you suggested) the relevant mechanisms are complicated and AFAIK not completely understood. Other factors besides metabolism may also come into play.
I suppose this article is a reasonable start:
https://en.wikipedia.org/wiki/Blood-oxygen-level-dependent_imaging
Despite these reservations fMRI remains popular, at least in part because it is non-invasive and is one of the few tools we have for studying humans.Edit: more disclaimers. :-)