Both vim and the Sublime Text editors are configurable on whether they use spaces or tabs for indenting and whether they convert existing tabs to spaces (or vice versa) or not.
For vim, see this question on vi & vim StackExchange. Basically, if you always want spaces instead of tabs, add set expandtab to your ~/.vimrc file. If you want to convert existing tabs to spaces, type :retab when in command mode.
For Sublime Text, see this part of its reference documentation. Basically, you probably want to set detect_indentation to false to prevent Sublime from attempting to adapt to the existing practice within each file you load, then set tab_size, use_tab_stops translate_tabs_to_spaces, auto_indent and trim_automatic_white_space according to your preferences.