Short answer:
The key point is to tell emacs to insert whatever you want when indenting, this is done by changing the indent-line-function. It is easier to change it to insert a tab and then change tabs into 4 spaces than change it to insert 4 spaces. The following configuration will solve your problem:
(setq-default indent-tabs-mode nil) RET
(setq-default tab-width 4) RET
(setq indent-line-function 'insert-tab) RET
Explanation:
From Indentation Controlled by Major Mode @ emacs manual:
An important function of each major mode is to customize the key to indent properly for the language being edited.
[...]
The indent-line-function variable is the function to be used by (and various commands, like when calling indent-region) to indent the current line. The command indent-according-to-mode does no more than call this function.
[...]
The default value is indent-relative for many modes.
From indent-relative @ emacs manual:
Indent-relative Space out to under next indent point in previous nonblank line.
[...]
If the previous nonblank line has no indent points beyond the column point starts at, `tab-to-tab-stop' is done instead.
Just change the value of indent-line-function to the insert-tab function and configure tab insertion as 4 spaces.