With pressure canning, you need a minimum water level before you start. I have a 30 quart pressure canner and usually add three or four pints more than the minimum level shown in my canner. I find this helps stabilize the temperature as well as make sure I have plenty of water for steam. More mass should equal more stable heat. With pressure canning, I don't think it matters if the jar is covered or not. I've done it both ways.
Headspace and removing the air bubbles are important. I use a plastic knife to remove the air bubbles. I tried using a plastic chopstick but it was too thick for some things, like pickles and green beans. The plastic knife works well for me.
Are you using a gauge or one of those weights set at a certain pressure? If you are using a weight, you shouldn't have this problem, but a big pressure swing, way high then low, can cause the contents to come out. My altitude adjusted recommended pressure is 11 pounds. I use a gauge and try very hard to keep the pressure between 11.5 and 12.5 pounds. Sometimes it is harder than others. I don't know why.
When the process is over, do you let the pot cool on its own? You need to keep the pressure canner closed until the pressure drops to atmospheric on its own. When time is up, I move the pressure canner off the eye and let it cool. Once it drops, I usually wait 10 more minutes to take the lid off, just to make sure. If the pressure drops too fast, the product will come out.
How tight are your rings? They need to be tight without being really tight. I crank them down fairly tight but don't overdo it. Some excess air in the jar needs to escape so it will seal, but too loose and you can lose product. Hard to explain.
I also use new lids and reuse the rings. I inspect the lids when I wash them but have never found one that was damaged. I have found brand new rings damaged, though.
Hope this helps some.
