Who should carry out leak testing?
Testing should be planned by someone who understands the façade system, such as a façade consultant or the professional overseeing the repairs, and carried out by a team that can access the façade safely and observe from inside. The test method, sequence and results should be documented with photographs so that the repair addresses what was proven.
From the RRD Field Guide, checked against the sources cited in Façade and Curtain Wall Water Leakage: How to Diagnose and Fix the Root Cause. General information, not advice for your project.
The fuller picture
Façade leaks are diagnosed by mapping when and where water appears, ruling out non-façade sources, then reproducing the leak with controlled water tests: AAMA 501.2 nozzle testing for curtain walls and ASTM E1105 pressure-chamber testing for windows and walls. Test from the bottom up, isolate one joint at a time, and repair the proven path rather than re-sealing everything.