My guess is that what you did wrong was to leave a rough spot inside the hole and you had a paint build up around that rough spot. When you pushed in the tube you scraped away the paint around the rough spot.
I claim some experience and success on this issue. I've made over 10,000 acrylic pens over the last four years and I've back painted every one.
1. Your drill bit needs to be very sharp so it doesn't leave rough spots to catch paint build ups, use a file to smooth out the inside of the blank before painting.
2. I don't use a larger bit, but not all recommended bits are made at the correct size.
3. I use acrylic craft paint and match the colors, I use a q-tip for a brush, and I use the paint right out of the bottle, no thinning. Spray paint works just as well, probably better, but I have about 120 colors of acrylic paint and I can't find spray paint in that many colors.
4. I use thick CA to glue tubes. CA does not dissolve acrylic craft paint. Epoxy works just as well, but it is much slower. With CA it takes some practice to insert a tube in a snug fitting blank hole without getting it stuck half way in, once you start pushing it in, don't stop until it is all the way in.
5. I never paint the tubes. That would be like wearing two seat belts, just in case.