Rim issues

Having some issues with a new wheel.  It's a cheapy I bought online and mated a cassette with it to use on the trainer.  Since it was raining here today I decided I would finally put my trainer tire on and get to work inside.  The trainer tire is a pain in the butt itself, but then I couldn't get it to sit correctly on the rim.  After both beads of the tire were in and with the tube inflated it looked like one side of the tire was caved in - so if I were to put it on the flat spot it looked like the tire was flat, but the bead was down in the inner channel of the rim. 

I went ahead and inflated the tube to full pressure anyway to see if things would settle and the tube would eventually push the tire out.  Not so much.  About 10 minutes later there was a loud pop and hiss, the tube had popped. 

Not sure what is going on here.  I installed rim tape, but since it's only a single wall wheel I had to push it down in to the channel.  I got out the tape measure and as far as I can tell the rim is the correct size. 

This would probably be a lot more help if I posted pictures...  However, any ideas on what I'm possibly doing wrong would be greatly appreciated!