When the temperature reaches that 100 million K value, the helium reaction kicks in very quickly. Takes only a few hours for the initial burning. Called a helium flash . Core heats up so much it expands against the force of gravity. Hydrogen burning shell also gets pushed out, but that lowers its temperature so the burning rate goes down.
Net result is that luminosity goes down because total rate of energy goes down.
Star starts contracting again, surface temperature increases. Stable helium burning sets in. For low-mass stars, the energy generation in the core is always about the same, so they all have the same luminosity. Outer layers will be different, depending on how much mass they lost during the red giant wind phase. Stars that lost a lot of mass will have smaller radii and higher surface temperatures than stars that didn't.