Are "thread-safe" functions parallelization framework dependent?

I have this simple MATLAB code which calls imregionalmax in a parallel loop over 256 pathces of 16X16 pixels.

function y = Parimregionalmax(x)
   assert(isa(x,'uint8'));
   assert( all(size(x)==[16 16 256]) );
   y = zeros(size(x));
   parfor k = 1:size(x,3)  
     y(:,:,k) = imregionalmax(x(:,:,k));
   end
end

Giving this code to MATLAB's Coder gives the following C code:

/*
 * Parimregionalmax.c
 *
 * Code generation for function 'Parimregionalmax'
 *
 */

/* Include files */
#include "rt_nonfinite.h"
#include "Parimregionalmax.h"
#include "libmwimregionalmax.h"

/* Function Definitions */
void Parimregionalmax(const unsigned char x[65536], double y[65536])
{
  int k;
  int i0;
  int i1;
  double imSize[2];
  unsigned char varargin_1[256];
  boolean_T conn[9];//unsigned char 
  double connSize[2];
  boolean_T BW[256];

#pragma omp parallel for \
 num_threads(omp_get_max_threads()) \
 private(i0,i1) \
 firstprivate(varargin_1,imSize,conn,connSize,BW)

  for (k = 0; k < 256; k++) {
    for (i0 = 0; i0 < 16; i0++) {
      for (i1 = 0; i1 < 16; i1++) {
        varargin_1[i1 + (i0 << 4)] = x[(i1 + (i0 << 4)) + (k << 8)];
      }
    }

    for (i0 = 0; i0 < 2; i0++) {
      imSize[i0] = 16.0;
    }

    for (i0 = 0; i0 < 9; i0++) {
      conn[i0] = true;
    }

    for (i0 = 0; i0 < 2; i0++) {
      connSize[i0] = 3.0;
    }

    imregionalmax_uint8(varargin_1, BW, 2.0, imSize, conn, 2.0, connSize);
    for (i0 = 0; i0 < 16; i0++) {
      for (i1 = 0; i1 < 16; i1++) {
        y[(i1 + (i0 << 4)) + (k << 8)] = BW[i1 + (i0 << 4)];
      }
    }
  }
}

/* End of code generation (Parimregionalmax.c) */

As you can see, the generated code (which works perfectly) uses openmp parallelization framework and calls the function imregionalmax_uint8 which is implemented in a separate "black-box" dll (with corresponding header and lib files).

Can I assume that this fuction is always thread safe no matter which parallelization framework I use?

Examples:

1.Is it OK to define two threads using C++ <thread> library in a console application (a.k.a exe file in VS) and call from each thread to imregionalmax_uint8?

2. Do two separate dlls (loaded by exe file) can call this function simultaneously?