The discontinuity in lon where it changes from +180 to -180 causes the problem with pcolor, which you see as the blue streak in the upper part of the plot. The pcolor documentation says that, in order "to create a rectangular grid of vertices", if input X is a vector it must be "A vector containing values that are increasing or decreasing". With that discontinuity, the values of lon are not all-increasing or all-decreasing.
A simple way fix the pcolor plot is to plot based on a sorted copy lon and a copy of mync where its columns are rearranged in the same order. See lon_plot and mync_plot below.
% Repeating the first part
load cpc.mat
lat = double(lat);
lon = double(lon);
mask = lon > 180;
lon(mask) = lon(mask) - 360;
lat = flip(lat);
tmax = flipud(tmax');
% Repeating making a new netcdf file
file_name = 'new.nc';
ncid = netcdf.create(file_name, 'NETCDF4');
lat_len = length(lat);
lon_len = length(lon);
lat_dim = netcdf.defDim(ncid, 'lat', lat_len);
lon_dim = netcdf.defDim(ncid, 'lon', lon_len);
lat_var = netcdf.defVar(ncid, 'lat', 'double', lat_dim);
lon_var = netcdf.defVar(ncid, 'lon', 'double', lon_dim);
tmax_var = netcdf.defVar(ncid, 'tmax', 'double', [lat_dim, lon_dim]);
netcdf.endDef(ncid);
netcdf.putVar(ncid, lat_var, lat);
netcdf.putVar(ncid, lon_var, lon);
netcdf.putVar(ncid, tmax_var, tmax);
netcdf.close(ncid);
% Visualize
mync = ncread('new.nc','tmax');
lat = ncread('new.nc','lat');
lon = ncread('new.nc','lon');
figure(1)
subplot(2,1,1)
[lon_plot,idx] = sort(lon);
mync_plot = mync(:,idx);
pcolor(lon_plot, lat, mync_plot)
title('Cartesian Axes with pcolor()')
colorbar
shading interp
axis equal tight
grid on
subplot(2,1,2)
axesm('eqdcylin')
pcolorm(lat, lon, mync)
title('Map Axes with pcolorm()')
colorbar
shading interp
tightmap
gridm
mlabel('south') % Longitude tick labels
plabel('on') % Latitude tick labels
