The basic issue is that there is no automatic reset of the Mini Pro when the serial line becomes active.
Here is the process that I use:
1. Start the compile/download cycle
2. At some point the 'Rx' LED on the MiniPro will flash.
3. Press the reset button when this happens.
4. The bootloader will take over on reset and allow the download to be executed.
It can be a bit tricky, but like most of these things the timing will comm with practice
An alternative is to modify the Pro Mini woith a capacitor (from memory) that reset the serial line. You can search for this using google.