It depends and is very not straightforward. Most OMMs that you would trade with are closer to HFT stock traders rather than vol traders.
Let's ignore those. Among vol traders (MMs that would keep meaningful positions in gamma or vega overnight), guys making markets in liquid products would usually analyze of the current markets and make adjustments based some richness/cheapness model. Guys who are making a market in something illiquid (where liquidity is low compared to the requested size) would frequently start with realized vol and go from there