Default templates in Visio don't seem to work the same way as Word nor Excel. It appears you will need to create a template and then always select that particular template when creating a new Visio document.
Now you have worked out how to customise a style, the hard part is done. You should Save As a template using the document you already customised the style in. Set up the contents of that template properly so that it includes your preferred stencils, styles, colour scheme, backgrounds etc. You can also create custom stencils containing your preferred shapes or create new ones for reuse (like including your company logo).
See
https://support.office.com/en-ie/art...c-4edea8bb72e6 for some other info on setting up and using a template.