Wow, first of all, get rid of those tires, they SUCK!!!! I tried them and they are terrible. Conti Ultra sport bottom of the barrel junk.
I have decent reults with Conti Ultra Race at a minimum. Also check out Serfa Seca ($25 at REI). Good tires but you may want the 25 as the run a bit narrow.
The tube pics are either very cheap tubes or you are missing the tire liner in th rims. That is a serious blowout which could have been casued by the spoke holes inside the rim sucking in the tube. Most stock rims come wiith CHEAP rim strips. Plactic or rubber that move exposing the holes. Get Velox or similar (medical like cloth tape) for rim strips, it's adhesive and stay in place.
This is the Performance brand of rims strip. Similar to Velox. I use it and it works just as well.
http://www.performancebike.com/bikes...1604509_400941