"When people say they're looking to grow by an order of magnitude they usually mean ten times." I think this gives "people" too much credit. In my experience when people say they're looking to grow by an order of magnitude, they don't know that has a very specific meaning and they're just talking about getting bigger by some vague undefined number that could be anything from about two times on up.
Not saying you're wrong, but in my experience I only hear this phrase from technical people, and my understanding is they always mean base 10. Which was surprising to me cause in my CS education I was basically taught to forget base 10 and only think in 2s).
I don't even really blame them, because I'm sure they simply hear the phrase a few times from technical people without explicit explanation of meaning and then adopt it themselves to mean "any big growth" which is a fairly reasonable assumption contextually, prior to someone pointing out to them that it means something more specific.
FWIW, in my CS education (both at school and self-directed via books, system manuals and such) I was taught to worry about whatever base is relevant to my current data and level of abstraction to the machine. 2, 10, 16 and even 8 were the usual culprits, but certainly nobody tried to teach me to forget about the ones other than 2. I worry about base 2 far less than base 10 in my day to day code despite the fact that I'm old and know assembly (6502, 68k, x86, MIPS, ARM) and still do a lot of bit-twiddling.