What kind of tires did they consisder flimsy?Brand, model?
Do you know how much air was in your tires? If the air pressure was low, it's possible you got a snakebite aka pinch-flatted. If you can check the tube that blew, look for two holes next to each other (looks like a snakebite - hence the name"snakebite"). If you go over a bump with not enough pressure in the tire, the tire can bottom out, squishing the tube enough to pinch it between the rim and ground and cause a flat.
I doubt it had anything to do with your changing the tire. If there was tube between the rim and tire, it'd have blown sooner. To make sure you don't have that problem, after you change the tire, hold it out in front of you and spin it around, checking both sides to make sure the tire is seated in the rim evenly all around. You should do that after putting just enough air in the tube to give it shape, then when you know its okay, fill it the rest of the way. If you see some of the tube protruding, let the air out right away! Then just redo it till you've got it right.
The more times you change a tire, the easier it gets. Definitely a good thing to know how to do, especially if you do much riding alone.
Time is a companion that goes with us on a journey. It reminds us to cherish each moment, because it will never come again. What we leave behind is not as important as how we have lived." Captain Jean Luc Picard