It's normal for some water to trickle from the tank into the bowl while the tank is filling. If the tank is done filling and water is still draining into the bowl, that is a problem with the flapper. The flapper might need to be cleaned, or the rubber might be stiff and dried out.

Turn off the water to the toilet and flush. Take the tank cover off, lift the flapper and and inspect the underside and the drain surface that it seals on to for any buildup and wipe clean with a rag. My water leaves clay deposits, so I have to clean gray goo off my flapper ever couple of years.

If the flapper and its mating surface are clean, then it is no longer sealing and the rubber flapper needs to be replaced.