Wastegate doesn't "dump" anything anywhere, it bypasses exhaust gasses around the turbo impeller in order to limit boost.
Dump valves are something completely different (and also totally pointless on diesels), they "dump" airflow to atmosphere (hence the pshhhh noise, though the better ones actually recirculate the air, but are virtually silent so boy racers on't like them) when the throttle is closed. On a petrol engine there is a physical throttle choke/flap tat will stop the airflow, diesels don't have one. If the airflow is stopped the turbo will stall (ie stop) and when the throttle is reapplied there will be greater lag (ie takes longer to get boost back as the turbo spools up). On a diesel as there is no throttle choke the air just goes into the cylinde as usual, actually helping to maintain turbo turbine speed as the volume of exhaust gases stays high, whereas on a petrol the exhaust gas volume an speed drop off sharply.
As an aside a couple of seasons back M-Sport and Pro-drive on the Focus and Impreza respectively introduced a boost recovery system whereby, any excess pressure was diverted to a large storage tank (in the rear bumper on the focus IIRC), when needed this air could be used to supplement the turbo at times of low boost hence helping to reduce the lag effect.