To continue on with this...
OK, first, basaltic rocks are formed constantly along the ocean's trenches and places like Iceland and the Ring of Fire. Those are the ones caused by tectonic plates. Mafic Basalt and Gabbro should form from rocks that are taken pretty much straight out of the magma sea, while felsic stones like granite would form in chambers allowed to cool down over long periods of time.
Secondly, the Earth's molten core constantly sends up plumes of hot molten magma which are less dense and rise to the "surface" of the mantle, cool down, become more dense, and then sink. This occasionally results in some magma getting thrust up into the weak points in the Earth's crust and causing pressure to build in magma chambers and erupt even without the tectonic plates being involved. (Of course, this action is also the cause of the tectonic plates in the first place, so I guess it's not to say that they aren't involved.)
Thirdly, I'm not sure why we're saying that DF's world doesn't have tectonic plates - other than the fact that worldgen is too short to make continental drift not have meaning, is there any reason why not? We already have volcanoes in-game, so it seems a little strange that we would say there aren't any cases of magma being thrust up to the surface.
Fourth, on the specific case of magma not cooling, we're talking about it NEVER cooling. As in, a 2/7 magma tile can melt hundreds of metric tons of objects and remain out of contact with the heat of the planet's mantle for as long as your fortress runs (and some people run 50+ year fortresses) without convecting in the least or even gaining more mass. There is space for additional realism, here.
As for mafic vs. felsic magma, the "mafic" part refers to Magnesium and Ferric (I.E. Iron) and mafic magma has both of those metals in abundance. The magma from the core of the Earth has mafic qualities, but if magma gets trapped into magma chambers, then it will gradually start cooling, and the magnesium and iron will solidify first because they have higher melting points, leaving behind the mostly siliceous materials.
Granite (felsic intrusive) is less dense than basalt, and as such, "floats" on top of magma better, letting it be more thick, and rise above the basalt. Most continental rock rests on a bed of granite, while the oceans have a much thinner crust of basalt.
Most volcanoes like in Iceland or Hawaii or in the deep sea trenches have mafic magma that just constantly erupts. Felsic volcanoes, however, tend to be like Mt. Vesuvius - they take hundreds or thousands of years of constantly building up extra magma and pressure to eventually blast away tons of rock explosively in pyroclastic felsic rock explosions. Mt. Vesuvius destroyed Pompeii before the people could even react. You can out-walk an eruption of a Hawaiian volcano.
The intermediate stones are simply formed by magma that had not cooled off all its iron and magnesium yet, or where a pocket of felsic magma was mixed with a new upshoot of mafic magma from below.
Ultramafic is extraordinarily rare to occur in the current state of the Earth, but existed in the ancient past before the crust of the planet fully cooled off. Today, the only real vestiges of ultramafic rock are deep near the mantle of the Earth, or in a few special Kimberlite pipes. (These are, notably, where most of the world's diamond mines occur.)
To properly model this, magma from the magma sea should be mafic, while magma pipes or volcanoes would potentially be any of the three. (This might require some sort of additional data put on the magma itself, however, so I'm not sure if Toady would be ready to do this.)
I have a thread on
geologic structures from back when Toady requested more data on geology for the 3d ore veins concept. If anyone's interested in more, it's a place to look.