? Is it a conflict for the persons or company, that install the low voltage wiring - to certify and test they our work ?

From the information listed below, in my opinion, I believe it could.

By definition the switch wiring, is part of the distribution system.

Distribution system shall be Inspected (see 5.1.12.3.) and Verification 5.1.12.4

Chapter 3 Definitions

3.3.143  Piped Distribution System. A pipeline network assembly of equipment that starts at and includes the source valve, warning systems (master, area, local alarms), bulk gas system signal actuating switch wiring, interconnecting piping, and all other components up to and including the station outlets/inlets. (PIP)

5.1.12.3  System Verification.

5.1.12.3.1.4  Testing shall be performed by a party other than the installing contractor.