That indeed seems to be the case. The Australian MSDS for the Ilford / Harman
Warmtone developer additionally mentions a significant amount of 5-10% borax, and a small (<1%) amount of a substance called "1-Phenyl-4-methyl-3-pyrazolidone", which according to
this page is a developing agent too. According to Wikipedia, one of
borax's uses is to buffer solutions at a certain pH (usually pH 8, just mildly alkaline, but I see also a mention of pH 9.2-11 for a
buffer with borax and sodium hydroxide, so that may be possible too). Anyway, the Warmtone developer may not be more alkaline after all, but buffered at a slightly lower pH, more close to neutral pH, compared to the Cooltone and normal Multigrade developer. That would be in accordance with John's remark.
Of course, with pH being a 10log of H+ ions concentration, even a 1 step difference in pH, means 10x more or less alkaline hydroxide (OH-) ions in solution to participate in the development process, so even an apparently "small" change of pH from 10 to 9, could have a significant effect on developer activity.
By the way, the MSDSs of course also mention Hydroquinone as the actual developing / reducing agent in all the variants, I just didn't list it in the previous post, as it seemed logical enough and there aren't differences in the sheets (all mention 1-5%)