We analyze hydrodynamic fluctuations of a hybrid simulation under shear flow. The hybrid simulation is based on the Navier-Stokes (NS) equations on one domain and dissipative particle dynamics (DPD) on the other. The two domains overlap, and there is an artificial boundary for each one within the overlapping region. To impose the artificial boundary of the NS solver, a simple spatial-temporal averaging is performed on the DPD simulation. In the artificial boundary of the particle simulation, four popular strategies of constraint dynamics are implemented, namely the Maxwell buffer [Hadjiconstantinou and Patera, Int. J. Mod. Phys. C 08, 967 (1997)IJMPEO0129-183110.1142/S0129183197000837], the relaxation dynamics [O'Connell and Thompson, Phys. Rev. E 52, R5792 (1995)1063-651X10.1103/PhysRevE.52.R5792], the least constraint dynamics [Nie , J. Fluid Mech. 500, 55 (2004)JFLSA70022-112010.1017/S0022112003007225; Werder , J. Comput. Phys. 205, 373 (2005)JCTPAH0021-999110.1016/j.jcp.2004.11.019], and the flux imposition [Flekkøy , Europhys. Lett. 52, 271 (2000)EULEEJ0295-507510.1209/epl/i2000-00434-8], to achieve a target mean value given by the NS solver. Going beyond the mean flow field of the hybrid simulations, we investigate the hydrodynamic fluctuations in the DPD domain. Toward that end, we calculate the transversal autocorrelation functions of the fluctuating variables in space to evaluate the generation, transport, and dissipation of fluctuations in the presence of a hybrid interface. We quantify the unavoidable errors in the fluctuations, due to both the truncation of the domain and the constraint dynamics performed in the artificial boundary. Furthermore, we compare the four methods of constraint dynamics and demonstrate how to reduce the errors in fluctuations. The analysis and findings of this work are directly applicable to other hybrid simulations of fluid flow with thermal fluctuations.