He means, take a big breath and tighten up as you bring your hips down and shins against the bar. I wouldn't say a strong valsava part is that necessary for a clean as you are using a very small weight in comparison to you dead. But the "clamping down" and getting into a mechanically strong position is very important.
Part of the problem is the shorts you're wearing, they're so long that I think it's causing you to subconsciously keep the bar away from your legs as you pull it off the ground. Ideally, your shorts for squats and pulls should stop above the knee. In other words, you need to do a better job keeping the bar in close against your legs on the way up.
Second, you need to keep your hips back longer. You're letting your body get upright too soon. Think of your torso as a lever with your hips as the fulcrum (very similar to a trebuchet, really); if you are too upright, you lose all that potential leverage that you can use to fling the bar up.
Third, you need to smooth out the transition through the middle of your pull. You can see that the bar is pausing for a split second when it reaches your thigh as you're about to propel it up. Pull the bar slower off the ground and up the shins to help smooth this part out.
If you keep the bar close to your legs and close to your body all the way up, and you focus on pulling the bar straight up, then you won't have to jump back to catch the bar in balance.
Mike, thanks for the answer. Apart from my shorts getting it the way, I've caught my knees few times so I'm concious about them. I'll try slower off the ground next time and see how it goes. About the upright torso - I didn't even realize that part. I always thougth of PC as a deadlift that you have to pull, shrug, jump and catch hehe. Thanks for putting it right for me.
You might find it easier to point your feet and knees out a bit and initiating the pull with your quads instead of your hips. I think of the first pull as pulling my knees back. It'll be easier to get your knees out of the way like this.
The bar should just brush your thighs at the spot where they hang while standing up straight. Right now you touch about 2 inches above your knees, when the bar hangs a good 2+ inches above that. Be patient, and the bar will not only go higher but it will travel in a more vertical path, so you can just squat down to catch it instead of jumping back.