I am displaying few links in an inline visualforce page. In Salesforce 1, when i try to click these links, it appears that the whole visualforce page opens up again with only these links and then users have to click again on the link to navigate further. Is this the known behaviour of inline visualforce pages in sf1 ? Is there any alternative for this ?
This is a "Working As Designed" scenario. The Visualforce page is masked as a preview by the Salesforce1 app and the only thing it can do when you tap on the inline page is navigate to the full page before you can interact with any content. There is no way around this unfortunately.
For reference in the Help & Training portal: https://help.salesforce.com/apex/HTViewSolution?urlname=Salesforce1-Embedded-Visualforce-pages-are-only-interactive-once-selected&language=en_US
When using Salesforce1 it is good practice to remember that any embedded Visualforce pages in a standard layout will have to be selected first before they can be interacted with. Once the user taps/selects the page, they will be taken to another page inside of Salesforce1 where they can then interact with the page and will then need to tap the back button to return to the details view.