I have never used Sublime Text 3, but I don’t think the following has changed since Sublime Text 2.
What you want to achieve is actually a standard feature in Sublime Text. You just have to turn it on.
This line from your the code you quoted …
{ "key": "setting.auto_complete_commit_on_tab", "operand": false }
… means “only execute the command if the setting called ‘auto_complete_commit_on_tab’ is set to false”. So simply turn on that setting.
In Default/Preferences.sublime-settings:
// By default, auto complete will commit the current completion on enter.
// This setting can be used to make it complete on tab instead.
// Completing on tab is generally a superior option, as it removes
// ambiguity between committing the completion and inserting a newline.
"auto_complete_commit_on_tab": false,
Put "auto_complete_commit_on_tab": true in User/Preferences.sublime-settings. Both mentioned files can be accessed via the Preferences menu.