The genius of the 555 design is that it is based on ratios of components, not their absolute values. When charging up a capacitor through a resistor, it takes one time constant (resistor value times capacitor value) to reach 63% of the power supply voltage. Thus, with a 15 V supply it takes one time constant to reach 63% of 15 V. with a 6 V supply, it takes one TC to reach 63% of 6 V. So, if the internal comparators also are working with percentages of Vcc for their trip points, they are comparing one varying percentage of Vcc (the capacitor voltage) to one fixed percentage of Vcc (either 33% or 67%, depending on the comparator). Because everything is based on percentages of Vcc, everything tracks even when Vcc changes.
Overall, the 555 acts as a relaxation oscillator with one huge difference. The standard relaxation oscillator usually changes state when the capacitor voltage reaches a specific value based on the device physics. Examples of this are a neon bulb or a unijunction transistor. With the 555, the trip points are based on three resistors, not the forward or reverse voltage of a semiconductor. Accurate resistor values within an IC require laser trimming, a very expensive process step. But accurate resistor *ratios* are easy and cheap, because they fall out of the standard IC fabrication process. While the absolute values of the 555 resistors are not very accurate, their ratios track to within 1%, including temperature drift. Working within the limitations of early 1970's IC fabrication, this was pure genius.
ak