Like the warning says, you cannot manually set the position of something controlled by a TiledChartLayout.
However, you can avoid using tiledlayout and instead create the axes explicitly and then move them and the colorbar wherever you want.
For example:
% Create a data sets
data = rescale(peaks,0,600);
data1 = rescale(peaks,0,700);
newTickVals = [3 25 300 350 450];
limits=[newTickVals(1) newTickVals(end)];
x=1:1:49;z=ones(size(x));
f1=figure('Position', [0 400 1500 500]);
% Tile 1
axes( ...
'Parent',f1, ...
'Units','normalized', ...
'Position',[0.05 0.05 0.35 0.9]);
contourf(data,newTickVals,"ShowText","on")
C=colormap('parula');
colormap(flipud(C))
clim(limits)
colororder({'r'})
yyaxis right
plot(x,z,'red',LineWidth=2)
ylabel('\bf Z values','Color','r','FontSize',18)
% Tile 2
axes( ...
'Parent',f1, ...
'Units','normalized', ...
'Position',[0.5 0.05 0.38 0.9]) % width after adding cbarf becomes 0.35
contourf(data1,newTickVals,"ShowText","on")
C1=colormap('parula');
colormap(flipud(C1))
h2=cbarf(data1,newTickVals);
set(h2,'Position',[0.9 0.1 0.02 0.8])
clim(limits)
colororder({'r'})
yyaxis right
plot(x,z,'red',LineWidth=2)
ylabel('\bf Z values','Color','r','FontSize',18)
