t = 1:0.1:10;
yyaxis('left');
plot(t, sin(t), 'b.-', 'LineWidth', 2);
ylabel('sin');
text(4,0.5,'left=0.5','BackgroundColor','y');
yyaxis('right');
plot(t, cos(t)*2, 'g.-', 'LineWidth', 2);
ylabel('cos');
xlabel('Time[ms]');
text(4,0.5,'right=0.5','BackgroundColor','y');
yl=ylim;yticks(linspace(yl(1),yl(2),11)) % make grids align both axes
grid on;
Do what needs doing on each axis when there to begin with.
While what you had will work; it's a lot more trouble switching back and forth than finishing the job when there.
The specific problem in your code is the two lines
...
set(hText, 'Position', [4, 0.5], 'String', 'left=0.5');
...
set(hText, 'Position', [4, 0.5], 'String', 'right=0.5');
...
hText is the array of BOTH handles; each call sets the position of both in turn to the same place on the axis presently in focus. So, the last axis to have focus and the call wins.
BTW when allocating space for future graphics objects, instead of
hText = nan(1, 2);
use
hText = gobjects(1, 2);
which is expressly for the purpose.
