Max Andrews is a philosopher who started out with a Bachelor of Science in Religion (that's actually a real thing!) from the Liberty University in Virginia, which claims to the be the largest Christian university. He went on to get a Masters of Arts in Philosophy, also from Liberty University for which, of course, he wrote a thesis. The contents of his thesis have reappear in various guises, for example as articles on his blog and embedded in his (two?) public debates. (As noted in The King of Spades and the Strong Anthropic Principle, Max Andrews has changed his position a little in recent times, so even he may no longer concur with what I refer to below.)
I've been reading through his thesis and have come across (once again) his "four mechanisms" (here's a shorter document which refers to them - you could even listen to his lecture which mentions the mechanisms, if the link had worked). What Andrews argues is that there are four mechanisms that are necessary for an inflationary multiverse to produce a life-generating universe:
A mechanism that supplies the energy needed form bubble universes
A mechanism that forms bubbles
A mechanism that converts energy of the inflation field (by which he seems to mean inflaton field) to "normal mass/energy" (by which he means not Dark Mass and not Dark Energy)
A mechanism that leads to variation in the fundamental constants between universes
This is not an original Andrews argument. It's an argument that was raised by Robin Collins in The Teleological Argument, an essay that appeared in The Blackwell Companion to Natural Theology which was edited by our old friend William Lane Craig (and J.P. Moreland). This is a go-to book for wannabe apologists and quite possibly ought to be one for wannabe anti-apologists, since it collects together the best of the current defences of theism - on the grounds that we should always try to interact with the best form of any argument we might want to argue against. Unfortunately, the book costs in the order of $200, so I'm just going to work from Collins' own preliminary version of his essay.
Robin Collins quotes the Shaw Prize winning cosmologist, John A. Peacock, when he formulates the four mechanisms, although it does seem that he's only using Peacock's words with respect to the inflaton field related to the first mechanism, specifically the following words: "the vacuum acts as a reservoir of unlimited energy, which can supply as much as is required to inflate a given region to any required size at constant energy density". In Collins' view, the inflaton field has to "conspire" with Einstein's equations in order to form and populate bubble universes. There's no indication that he has cosmological support for this notion.
Andrews, however, quotes Collins and another couple of chaps, Axel de la Maccora and Boris E. Meierovich. To the former he attributes the following notion:
If inflation is not complete or efficient then the remaining energy density within the bubble must be fine-tuned to give the correct value distribution.
And to the latter:
Attempts to circumvent fine-tuning concerning the inflation field have focused primarily on describing what occurs posterior to the moment of bubble inflation.
With respect to de la Maccora's attribution, it is true that Maccora said something very similar in the referenced paper, but look at the context taken from the abstract (my emphasis):
If the inﬂaton decay is not complete or suﬃcient then the remaining energy density of the inﬂaton after reheating must be ﬁne tuned to give the correct amount of Dark Matter. An essential feature here, is that Dark Matter-Inﬂaton particle is produced at low energies without ﬁne tuning or new parameters.
de la Maccora immediately follows the referenced sentence with a clear indication that fine-tuning is not required, a conclusion that can be comprehended if one reads the actual text of the paper. For example:
However in our scheme the regeneration of φ takes place naturally without ﬁne tuning and, once the ﬁeld φ becomes nonrelativistic, when its mass mo > T, φ will decouple since nφ is exponentially suppressed.
The aim of this section is to show how a single scalar ﬁeld φ can account for inﬂation at early times and as Dark Matter at a late time, without any ﬁne tuning of the parameters.
In other words, this is cherry picking of an astounding quality.
As for Boris Meierovich, I have tried to find a sentence or a paragraph from which the notion attributed to him could be extracted, with no success. Perhaps someone with more time or sharper eyes can find it, but I note that even if this were to happen, this is just another example of cherry picking. Meierovich's paper also speaks against fine-tuning:
The parametric freedom of the theory allows to forget the troubles of fine tuning. In the most interesting cases the analytical solutions of the Einstein’s equations are found.
The equations (31,49) with the boundary conditions (50) are easily integrated numerically. The regular solutions are free from fine tuning. Moreover, the existing parametric freedom results in a great variety of possible configurations.
But there's more …
Let's go back to Collins' four mechanisms (via Andrews). The first mechanism needed to supply the energy to form the bubble universes, according to Andrews, is the fine-tuning of the "inflation" field. Someone more sceptical than I might suspect at this juncture that Andrews is deliberately equivocating over the term "inflation field". No educated person really doubts that inflation is an excellent solution to a number of problems with standard cosmology (although there are other solutions put forward by respected cosmologist that don't rely on inflation). What we don't really understand at this point in time is what the mechanism behind inflation would be. But there are speculative theories. The inflaton is associated with one of those. To put this theory into perspective, if you google "inflaton" and look really carefully, you'll see that there are only about 530 mentions of inflaton on the internet (none of which are Andrews, because he consistently misrepresents it as an "inflation field" and many are repeats so that unique mentions probably amount to no more than 160 - at least one of which was due to a typo).
Collins and Andrews really should be more forthcoming about how speculative the theories that they are hanging their arguments on are.
So, if current theories about inflationary multiverses are correct and if the inflaton theory is correct and the two qualified people quoted by Andrews in support of his argument are wrong about the substance of their papers (but not that which was cherry picked from those papers), then maybe we would be in a position to suggest that multiverses are fine-tuned. But even then, the claim that this is indicative of a volitional agent's design is no more than a brash appeal to ignorance - "we can't think of any other reason for this, therefore goddunnit".