Why is a future increase in solar luminosity by 10% supposed to have disastrous consequences for life on earth when the last 30% did not?
In this regard you can think that the Earth system is like a house with heating but no Air conditioning. Therefore, it has a powerful mechanism to stay warm when the solar illumination is weak (greenhouse effect), but it has no such powerful mechanism to cool down if the solar illumination is too strong.

In hour analogy, let's say you have used your heating to keep your house nice and warm at 22°C over winter, when outside temperatures were much colder than that. As the temperature outside goes up in the spring, you turn down the power of your heating, so to keep the house at 22°C. Now, a ~10% increase in solar power output would be equivalent to the point were the outside temperature surpasses 22°C. Therefore, even with the heating off, your house temperature will start to rise over 22°C for first time, an you can't do anything about it.

The heating mechanism of Earth the greenhouse effect, specially the one due to ${CO}_2$. But most important, is the thermostat that have kept Earth's temperature in the range of liquid water. This thermostat is based on the fact that an increase of temperature leads to and increase of silicate weathering, that in turn leads to a drop in atmospheric ${CO}_2$ concentrations, and therefore to a drop in temperature. This negative feedback counteracts any warming due to increases in solar irradiation.

However, that trick will work only until the point when there is no more ${CO}_2$ in the atmosphere. Then, any increase in solar irradiation will have a direct effect on temperature, and other amplifying feedback will kick in. In particular the greenhouse effect of water vapor: The higher the temperature, the most water vapour in the atmosphere. And water vapor is a very effective greenhouse gas, therefore, that will lead to further increases in temperature.

The following figure gives an idea of the different radiative forcings as calculated by the IPCC AR5:


However, those are relative to the year 1750. The total effect of green house gasses is about 155 W/m². That corresponds to a 45% of the total energy we receive from the Sun (340 W/m²). That would mean that if you take away all greenhouse gases you can counteract an increase of about 45% of solar power output. In other words, Earth can keep turning the heating down to keep the planet temperature stable as the Sun keeps increasing its power output. However, this calculation is very naive, because we can't remove all greenhouse gases (that would mean removing all the water too). The models you mention are more realistic in this sense and they suggest that the critical points is just a 10% of solar output increase, much closer than the 45% of my ultra-simplistic calculation above.

Said that, the references in that Wikipedia article doesn't seem to use models fully coupled with all the Earth's systems involved (carbon cycle, tectonics, methane, albedo feedback, etc.). Therefore, I would took that 10% value with a lot of caution. However, what is true is that at some point, if you increase solar power enough, the temperature controlling processes of our planet will be overwhelmed, and life on Earth's will face the bigger challenge ever for its subsistence.