Usually a laser is considered as a system that delivers a particular temporal dynamic generation regime, which can be tailored by means of cavity parameters or power. By introducing a concept of PT-symmetry, one can achieve different types of stationary regimes, for example, single-mode operation. In the present work we consider a coupled Raman fiber lasers interconnected by means of Mach-Zender interferometer. We numerically investigate such coupled fiber lasers within a full dynamical model based on nonlinear Schrödinger equation. Firstly, we show that nonlinearity induced phase stochasticity does not destroy PT-symmetry, but makes PT-symmetric regimes to exist in narrower region of parameters. We study dynamical properties of the generation regimes and find that depending on parameters (pump power and phase shift), different dynamical regimes have different parity-time properties. We show that by varying PT-properties one can switch between different dynamic regimes. We also show that if the pump power is fixed, and phase shift is changed from zero (a case of fully uncoupled cavities) to the maximum value, the laser transits from generation in PT-broken regime to a PT-symmetric generation. At the same time, the laser exhibits a simultaneous reverse transition from a turbulent to a laminar generation.