While Bilbo Baggins answer is already great, he did miss an important piece of information you gave us: The temperature of the planet. With this I was able to figure out its distance from the sun, assuming it is a sol analog and making some assumptions about albedo. Assuming your moon has an ice world appropriate albedo similar to Ganymede of 0.43 it would need to sit at 1.46 AU from the sun. This would only make the situation worse. Yet if I assume that the same heating process that keeps the domes warm, I assume geothermal heat from tidal heating, which will require a HUGE moon or a parent gas giant, rejuvenates the surface on a regular basis as it happens on Europa and Enceladus, assuming an albedo of 0.81 like Enceladus is reasonable. This would mean that the planet receives 40% more light than Earth due to its distace of only 0.85 AU from the sun.
If we now assume it has a very low axial tilt, an equatorial band where the light remains strong enough all year long to allow photosynthesis in the domes is conceivable. For domes in the lower latitudes, I suggest you look into chemosynthesis and the bizarre environment of the Movile Cave, where a perfectly healthy ecosystem has existed form millions of years without sunlight. Volcanism could supply the necessary chemicals to keep these dark domes running.
That the domes are maintained by some creatures opens the possibility that the plants either use a combination of chemo- and photosynthesis, have evolved to live with way less sunlight than Earth plants (extremely slow metabolisms similar to those found in some endolithic bacteria or the capability for hibernation like polar plants and animals do on Earth are options) or were genetically engineered for this environment if it isn't natural. As some guy said: "Life always finds a way."