I have tested the issue but I could not reproduce the problem you faced. The template is applied to all the pages of the search result. What I have tested:
- Create an search index (Administration > Search Indexes) and re-index.
- Create search result page and select the results template (test with custom and build-in templates).
- Create Search page, drop the Search widget and set the index to use, than set the Search result page.
- All the Result pages have one and the same layout and search templates.
What is the problematic template you have - Layout or Search template? Are they custom ones?
Do you want to have your say in the Sitefinity development roadmap? Do you want to know when a feature you requested is added or when a bug fixed? Explore the Telerik Sitefinity CMS Ideas&Feedback Portal
and vote to affect the priority of the items