Use basic.sty with lualatex and biber.
Use mystyle.sty with xelatex and biblatex.
To use basic.sty, have the line,
\RequirePackage{basic.sty}
in the header of the main LaTeX file. Also, make sure that the directory
texmf is in the TeX path. This can be done by setting the shell
environment variable, TEXINPUTS to the path of texmf. In bash one can
append the following line to the ~/.bashrc or ~/.bash_profile:
export TEXINPUTS=:$(realpath ~/.local/etc/texmf):
where the path ~/.local/etc/texmf is only used as an example. Note
that realpath is redundant here, but it's important to realize that
TEXINPUTS requires an absolute path. On Mac, realpath is not a default
bash command, so see
http://stackoverflow.com/questions/1055671/how-can-i-get-the-behavior-of-gnus-readlink-f-on-a-mac
or use a static path in the config file.