The sync process for contacts and calendar events with a supported app on your computer is a bi-directional or true sync process.
There is a way to replace on the iPhone with what is available in the supported application on your computer but not the other way around.
If the supported application on your computer includes contacts and calendar events and the same with your iPhone, with the first sync for this data you will be provided a merge prompt, which you want to select.
This is selected under the Info tab for your iPhone sync preferences with iTunes.