Versions

• Bitbucket Server 4.9.0
• SourceTree 1.9.6.1
• Windows 8.1
• Oracle JDK 1.8.101
• Git 2.10
• Internet Explorer 11
• Google Chrome

Behavior in Internet Explorer:

1. Navigate to the repository in Bitbucket Server
2. Click the Clone action
3. Click "Clone in SourceTree"
4. The following confirmation message shows up:
   
5. After clicking "Allow", the message "No apps are installed to open this type of link (sourcetree)" is shown:
   

Behavior in Google Chrome:

1. Navigate to the repository in Bitbucket Server
2. Click the Clone action
3. Click "Clone in SourceTree"
4. Chrome does absolutely nothing:
   

Workaround:

There are other ways to clone a repository into SourceTree mentioned here