Why is this deterministic variant of Miller-Rabin not working? I am using this paper as a reference.
The Miller-Rabin test, as classically formulated, is non-deterministic -- you pick a base $b$, check if your number $n$ is a $b$-strong probable prime ($b$-SPRP), and if it is, your number is probably prime (repeat until "confident.")
A deterministic variant, assuming your number $n$ is below some bound (say $n<2^{64}$), is to pick a small number of bases $b$, and check if $n$ is a $b$-SPRB relative to each of those bases. There seems to be a bit of a sport to finding very small sets of bases, so as to make this process as fast as possible.
In particular, the cited reference declares a theorem of Jaeschke and Sinclair, that 

If $n < 2^{64}$ is a $b$-SPRP for $b\in\{2, 325, 9375, 28178, 450775,
9780504, 1795265022\}$, then $n$ is a prime.

It doesn't state any extra hypotheses on $n$, or on what it means to be a $b$-SPRP. However, the classical formulation of Miller-Rabin only talks about $n$ being a $b$-SPRP when $b\leq n-2$, whereas the theorem above seems to allow $n<b$.
In particular, I have found (purely by accident) that $n=13$ does not satisfy the above criterion, meaning that as stated it gives wrong answers, and I don't know why (so I can't predict more of them).
So the question: Is this a shortened form of a proper theorem, where I should only be checking the values of $b$ where $b\leq n-2$? Is this an error in the paper? Am I just crazy?
For sake of completeness, the definition of $b$-SPRB I am using is the one given in the paper:
Factor $n$ as $2^sd$, where $s$ and $d$ are nonnegative integers and $d$ is odd. Then $n$ is a $b$-SPRB iff $b^d\equiv 1\ (mod\ n)$ or, for some $r$ with $0\leq r < s$, $\left(b^d\right)^{2^r}\equiv -1\ (mod\ n)$.

Not a duplicate of: Bases required for prime-testing with Miller-Rabin up to $2^{63}-1$ seems to lead to the same questions (they don't address the issue of when $n<b$; it's just irrelevant there) and uses bases so small it doesn't matter.

If you look at Best known SPRP base sets, you can see the remark "Depending on your Miller-Rabin implementation, you may need to take a ← a mod n." and "When the witness a equals 0, the test should return that n is prime."  The latter is saying we skip that test when n divides the base.
This is especially critical for making sense of the smaller base sets which generally have very large bases.
