On Linux subl is just a symlink or shell wrapper around sublime_text because on that platform they’re the same thing (whereas on Windows and MacOS, the vagaries of those platform require an additional helper program).
However, on my Linux boxes running sublime_text (or subl, which I manually symlinked because I also use the tarball version) just focuses the existing window unless I manually add -n to the end to tell it to create a new window.
How exactly are you invoking this? Are you doing it manually from a terminal, or from some sort of launcher? If the latter, your launcher might have additional arguments added to it or similar.