First, a quibble about jargon.
When a template is used, a new document is created from the template. When correctly used, the template is never saved as a document. I suspect you are, in fact, creating a new document and not using Save As.
Here is my page on Templates in Microsoft Word.
Now, as to your problem...
When a document is created from your template, check to see if the option is set to automatically update styles upon opening.
See [What happens when I send my document to someone else? Will Word mess up my formatting?] by Shauna Kelly.
You can check this setting in the Templates and Add-Ins dialog. One way to get to this is under the Developer Tab, click on the Document Template button. It is a checkbox, and you want it clear. If it is checked, open your template for editing (with the new document closed) and clear the checkbox in the template.