There's a heap of Surveyors paying their way just on Party Wall disputes ... so that should tell you something. There should have been a Notice served - so you and the Builder are off on the wrong foot already. Note though, that the builder, even though he should be in the "frame", is not the person you want to aim at ... it's the other owner. That's who ordered the work and who the dispute is with. Steer clear of "helping the builder", accepting" make good" etc etc , just for an easy life.
Party Wall disputes can excalate ...that's why many develop into: 1) Your Surveyor, (2) His Surveyor (3) A final arbiter Surveyor ( agreed by the other two to be judge and jury, essentialy...well make strong recommendations)
The best way out is for a Surveyor to be appointed - where both of you agree, he will make the fair arbitration on the issue. This is very normal. It is also normal for the guy to set out who pays his fees, how they are apportioned etc etc. In many cases, the instigator of the work will be obliged to pick up 100% of the Surveyor's tab.
Get an agreed Surveyor in .. and he can span out the right approach.
Neighbours CAN do a lot more excavating, on their side, than you think - and a neighbour can do some serious structural activity...before you can stamp up and down and shut him down carrying on reasonable development. However, there are very fair rules and guidelines on how to behave... and the affect on your property, in the future, is the main concern. An agreed Surveyor has the power to demand safety cash to be held in trust, a plan of works, inspection of "how it is now" and can oversee the verbiage and scope of any "guarantees" given