It's hard to tell what they're doing in the simulations you're comparing with. The climate simulation in Universe Sandbox is a latitude-dependent energy balance model, with one-dimensional heat transport in the equator<->pole direction. It accounts for the overall luminosity of the stars in the current simulation, and not their varying spectra (so far). There are a number of climate processes that can affect the boundaries of the habitable zone. I'll be writing a blog post to serve as some documentation of what is (and isn't) taken into account in the climate simulation in Universe Sandbox soon.