If NOT "at their lair", they are a (group of) "wandering monsters" (with a possible lair elsewhere, see rolling up a dragon at Overland scale). This places a +New Adventure Pin+ on the Overland Map, and it can MOVE (if not a "lair").

Meanwhile, the Dungeon/Site Exploration scale "Random Encounters" use the numbers listed in the Monsters Per Dungeon Level tables in the Dugan Design section of the DMG/Underworld book. As noted these numbers are much more like 1d8, 2d6, 1d12, etc.

It's (almost) the exact same procedure in hex-crawl mode as in dungeon-raiding mode. Ok, ok, here's they key piece from 0/1e:

All "seemingly too large" encounter sizes listed in the DMG monsters/npcs section are for Overland "Wandering Monsters" (Overland Random Encounters), and that's why it lists a % chance to find them at their lair.

The specific Random Encounter table used is given by overland-area/hex-type, OR specific adventure dungeon-level/exploration-area (or the general dungeon design RE tables in the GM material).

The rule-of-thumb is to have a "roster" of existing encounters in an area, and (almost always) to add whatever was rolled up to the roster. Then include those in the NPCs which take moves/counter-moves at the same time-scale as the players each "Turn".