Looks pretty simple - there must be a box gutter between the old roof and new one since the extension has one side of roofing abutting the old one. That means that the box gutter itself is too small or the outlets from it are too small (including if they are all trying to drain into a single 100mm or 90mm stormwater pipe as mentioned above).
In any case this is a problem your builder must remedy - by identifying the causes and redoing whatever needs to be done so there is no water going where it shouldn't. No ifs, no buts, it is your builder's problem - you do not need to know what the underlying cause or the solution is - just to firmly and persistently let him know that he has to fix it.
Advice from me on this forum is general and for guidance based on information given by the member posing the question. Not to be used in place of professional advice from people appropriately qualified in the relevant field. All structural work must be approved and constructed to the BCA or other relevant standards by suitably licensed persons. The person doing the work and reading my advice accepts responsibility for ensuring the work done accords with the applicable law.