why would overflow tube fill with water after flushing
It is normal for the refill tube to put water into the overflow pipe. It fills the bowl with new water.

The tank is filled by water coming out of the fill valve near the bottom of the tank.

It is not normal for the overflow tube to fill up with water. If it is filling with water, it is clogged. Run a wire or fish line or zip tie down the overflow tube to try to dislodge whatever is clogging it.