When creating new project from a custom or default template file, templates don't seem to load at all. Revit asks to choose units (metric/imperial) and after the project opens all the content that was saved in a template file doesn't load as well. The same with default templates.
Similar issue was discussed here, but it seems there wasn't a solution to the problem
http://www.revitforum.org/structure-general-questions/8739-help-revit-2013-template-problem.html
I found the solution. You have to add template file that you want to use to file locations in revit options. Then it works, otherwise it doesn't for some reason, even if you choose your file in a dialogue window that pops up when you are creating a new project.