You didn't mention the tubes you used...
I have found that Performance Tubes will do that. I bought several on sale and each blew out, I no longer buy them. Since the defect was near the stem, it's also possible you damaged the tube during inflation, also their maybe a defect or blur on the rim. Make sure you check you rim and rim tape.
I like Specialized tubes, the ones packaged in talc. More expensive but worth it.