A family of Microsoft word processing software products for creating web, email, and print documents.
A property will cascade only if the initial setting of that property in the dependent style is exactly the same as the setting in the based-on style.
One way to tell whether you've gotten them right is to look at the list of defined properties in the Modify dialog of the dependent style, just below the preview panel. If the property you want to cascade isn't listed there, then its value is inherited from the based-on style. If it is listed there, then its value is different, and the property won't cascade.
The colour setting is particularly pernicious. In the default setup, the property list for the Heading 1 style says "Font color: Accent 1", referring to one of the theme colours. What it doesn't tell you is that it's the "Accent 1, 25% Darker" variant. The Heading 2, 3, and 4 styles use the plain Accent 1, while Heading 5 and 6 use "Accent 1, 50% Darker." Thus changes in the Heading 1 colour definition won't cascade to any of the other Heading styles. If you want the colour to cascade, you must modify all the styles to use the same variant of the same theme colour or one of the non-theme (standard) colours.
The alternative, if you stick with the theme colours as in the default set of styles, is to select a different set of colours to use in the theme. On the Home tab, click the Change Styles button and choose Colors, then select a palette of colours that you find suitable or define a custom set. That will maintain the variants (darker/lighter) but switch the base colour for the Accent 1 and other selections. Similarly, you can choose different pairs of heading and body fonts by clicking Change Styles > Fonts, and the different sizes defined in the styles will be maintained while switching the fonts.