Tubes only blow out when there's someplace for them to blow out too. When things are right, the tube is constrained to the closed space within the tire and rim and cannot blow out.

So step one is to consider whether the space within the tire is a truly closed chamber. Possibly you have a hollow double wall rim, and the holes aren't covered properly (most common reason).

Step 2 is to look at the location and shape of the blowout. Belly side, near valve, long slot, or short pucker, etc. Compare that to the location on the rim and tire and see if it makes sense.

If the tape is in good shape and the blowout is a long slot, and the rim is narrow, then the issue may be that the tube is sticking within the tire and when initially inflated, stretches across the gap between the beads. Then with more pressure, that narrow strip stretches more as it blows down into the gap below. This is a common issue with narrow rims. See sketch and consider the effect of the area across the gap id the tube forms a circle, stretching down to fill the rim as shown.

There may be other causes, such as not properly seating the valve, but as I said, the process begins with looking at the tube to see where it's failing. That may tell you how and why.