it seems to me that the search module with google is using a deprecate api and currently is not honouring the siterestriction method.
Can anyone confirm this?
Yes, you are correct. There is old API which may be EOLed 1 Nov 2013. We have corresponding plans for implementing new API (PPB-14 for your reference) and we are working on it. But there are some inconveniences like 5000 requests per day limit or something else.
I haven't any ETA when it will be implemented.