This info seems to be stored in the hidden "XLimSpec" (or similar for y and z) property of the axes.
In Matlab R2016a:

>> figure;
>> axes;
>> get(gca, 'XLimSpec')

ans =

stretch

>> axis tight
>> get(gca, 'XLimSpec')

ans =

tight

>> set(gca, 'XLimSpec')
    'stretch'
    'tight'

What version of Matlab?  I find it strange that calling contour causes the axis limit modes to be set to manual.

I see a comment in the _contour_.m function that indicates that the reason for setting the axis modes was to avoid computing axis limits repeatedly as patches are added.  But now I'm wondering if we are doing this job incorrectly and should instead only be computing axis limits when rendering the axes or if explicitly requested.  For example, do the the following different in Matlab?  Note that these commands must be executed all on one line or in a script to avoid an implicit drawnow action when a command prompt is displayed.

clf; plot ([0, 10], [0, 10]); get (gca, {'xlim', 'ylim'})

clf; plot ([0, 10], [0, 10]); drawnow; get (gca, {'xlim', 'ylim'})

Only computing axis limits when rendering or when requested would improve efficiency generally and avoid the need for the kind of special code that attempts to defer computation of limits like we currently have in _contour_.m.

In this example

clf ; hold on
plot([0 10], [0 10])
[x, y, z] = peaks (50);
contour (x, y, z, -7:9);

the axes are scaled to [-3 3], clipping the upper part of the line. The correct behavior would be to merge the x– and y–domains, as done in Matlab.