Maccy,
Firstly don't worry about what happened, I think it's fair to say we've all turned lampshades (gone through the bottom of a bowl), and when learning it's all too easy to let the tool take over and what seems like a good, smooth running cut is not actually going where you want it to go. Time and experience will sort both those out.
For the undercut you were attempting.
When doing demo's at clubs, I sometimes pull out a bundle of barbecue (thin bamboo) skewers and use them to simulate the grain of the wood to show how the tool cut needs to be supported. saying 'Cut downhill', 'into the wood' etc., is not always the correct explanation.
If you have some skewers or drinking straws, hold them in a bundle and chop a 'U' shape into one end with the fingers of your other hand. Now look at the ends of the straws, if you are cutting from the rim, inwards, you are cutting over unsupported grain. You need to scoop out the bulk and then cut from the bottom of the undercut, up to the widest part of the timber to get a supported, smooth cut. It sounds counter-intuitive, but it does work.