You need to manually convert all the existing tabs to spaces in the document.
Changing the setting in your editor/IDE or on GitHub (to use spaces) does not change any existing text in the document. It only affects any new text you add to the document. If the existing content includes tab characters, you need to convert those to spaces for consistency. While you would need to manually change each instance on GitHub, your local editor/IDE should have a function to do that document wide from a single command (usually called something like "convert tabs to spaces").
By way of explanation, when a tab is inserted in a document, all that happens is a tab character is inserted. No information is included indicating how wide that tab character should be. Each document viewer will have its own setting indicating how wide a tab character should be and if those settings do not match, then the document will display differently in each context. For example, the GitHub editor can be configured to be different that the default. However, the rendered preview does not have any settings so you only get the default tab wide (8 chars on GitHub).
For that reason, most editors/IDEs include a setting to insert spaces when you type the tab key. That insures that every tab is exactly the same width across all viewers anywhere. However, the "spaces" feature of editors works by intercepting the press of the tab key on your keyboard and replacing the tab with the set number of spaces. Therefore, actual space characters get inserted into your document and there are no tab characters (the editor hides this by also intercepting backspace key presses). The important thing to note is that this feature works by intercepting and altering key presses on the keyboard. Therefore, it has no effect on text already in the document. Which is why you need to convert the existing text. Fortunately, the "convert tabs to spaces" feature of most editors/IDEs will use the tabs/spaces settings when doing the conversion, so running that command once should fix the entire document as long as your settings are configured properly.
Most editors/IDEs also have a "show whitespace" (or "view whitespace)" feature, which can be used to confirm the conversion was done properly. When "show whitespace" is turned on, tabs display as an arrow and spaces as dots (usually a lighter gray than the surrounding text). If you have converted your entire document. you should see no tab arrows anywhere, only dots for spaces. Once you are satisfied that no tabs exist, you can then turn "show whitespace" off. Unfortuntely, GitHub's online editor does not offer this feature, so you'll need to use your local editor.