But it can also really mean that way. One of the functions of the affix meN-kan is doing something for other people.
Example: Dia membuatkan ayahnya bubur. (He/she made porridge for his/her father)
In the example, the sentence structure S + V + OC + O also implies that the father did not ask for the porridge. The doer acted out of initiative (because the father is not able to do it by himself).
Whereas in "Dia membuat bubur untuk ayahnya," the father may have asked for his son/daughter to make porridge for him.
"She/He is writing a letter for/to her/his mom" is correct, tho there is another way and it is 'She/He is writing a letter "'for'" her/his mom'= Dia menuliskan surat "'untuk'" ibunya', so "for" could mean "untuk", and same for "to" meaning "kepada"
Thx for reading And sorry if my explanation is confusing