They raise the rates indirectly, by selling T-bills on the secondary market, which simply sucks money out of the circulation. (Which makes simply makes debt more expensive, and that leads to T-rate increase.)
> also the whole trope about 'China owning most of US T-bills' is actually false,
They are just the largest foreign holder, and it was noteworthy because of the rapid rise in the distribution of foreign debt holders.
Anyway, my thought process was that even if the US money supply drops, it should not influence T-bill auctions, because the whole world likes it (due to being the least risky investment). But it's very likely that the T-rate was low because banks and other investors exploited the low FFR. Now that's gone, the system settled in a higher equilibrium (as foreign and other investors had no real reason to change their behavior).