The 'sync collections' setting does not copy books or PDFs between devices - all it does is if you have the book on both devices and you move it into a collection on one of them, then it will be put into the same collection on the other device.
You will need to sync each PDF that you want on your phone. If you don't currently have them on your computer then connect your iPad to your computer's iTunes and do File > Devices > Transfer Purchases to copy them over (that should copy PDFs and/or epubs that are in the iBooks app, not just actual ibooks), and if using a Mac with Mavericks on it do File > Move Books From iTunes in the iBooks app on it, and you can then sync them to your iPhone.