Water flowing into the overflow tube suggests that the tank is not stopping at its intended level.
EPA's dye check can reveal a silent tank-to-bowl leak: add a small amount of food coloring to the tank, wait about ten minutes without flushing, and look for color in the bowl. Flush afterward to avoid staining. Follow the toilet maker's instructions for unusual models.
Keep this boundary: Do not assume a universal flapper fits every toilet. Tank design and manufacturer parts matter.