Most have built in overflow.
If you had to drain the main tank down to carryout the replacement you may have an airlock in the pipework to cistern this will need bleeding out.
Turn off the water feed to cistern then follow instructions for releasing the inlet valve washer assembly as if you would replace a washer then open the water feed slowly see if you get a steady splutter free flow. If it splutters let it run until it stops spluttering then you know all air is out. Most now work on tank or mains. By the way if you have no stopcock or check valve in the cistern pipework then fit one at same time.
BB
January 2010