They, along with the rest of the forageable goods, spawn in during the break between Saturday and Sunday. A side effect of this is that they will also remain in place until the end of Saturday, so if you see one and don't have your hoe, you can leave it for later. Unless it's Saturday, then you'd better get it. You can't really force the spawns, but the there is a hard cap of 6 items per map (the tidal pool seems to be an exception). So if you keep clearing the maps every one or two days, you can prevent them from capping and increase the average number of new spawns (each day the game tries to add 2-5 new items, but many of those attempts will fail due to illegal tiles). Of course, those spawns could be anything, there's no guarantee that they'll be worms.