It's easier to explain specifically if you post your prescription. But the
principles are that 1) every spectacle lens with focusing power has the side
effect of magnifying or minifying. 2) Lenses for (only) astigmatism have
power in one meridian only, stretching or shrinking the image in the
direction dictated by the orientation of the power meridian.

By "meridian" we mean a line across the lens, like 12:00-6:00 or 2:00-8:00
on the clockface.

If your glasses have (minus) power in the vertical meridian (12-6) and none
in the 3-9 meridian, objects will appear short and squatty, but not tilted.
If your lenses have minus in the horizontal meridian only, objects will
appear tall and thin, shrunken horizontally, but not tilted.

"Tilt" occurs when the power meridian is oblique, like 1:00-7:00 or
10:00-4:00.

The distortion is constant; it doesn't really change when you tilt your
head. Tilting your head probably brings the major distortion to a purely
vertical or horizontal meridian, where the distortion shrinks or magnifies
objects orthogonally, 12-6 or 3-9, without producing the visual "tilt" you
get at oblique angles. You can demonstrate this by folding up your glasses,
looking through one lens and rotating the lens around your line-of-sight.
The tilt will follow the orientation of the lens, and the vision will only
be sharpest at one orientation (actually two - upside down works also.)

And yes, usually your brain learns to re-interpret tilted images as "normal"
after a week or three. If it doesn't, sometimes we have to remake the lens
with less sharpness and therefore less tilt. Close-fitting frames produce
less distortion, just as a magnifying glass magnifies less when it's closer
to objects.

-MT

You can get the answer by looking in the mirror when you tilt your head.  You
will see that your eyeball does not tilt as much.  Therefore the orientation of
your eye to your head and your glasses changes.  It's the same as if you tilt
your glasses.  So the angle for correction of the astigmatism gets off a bit
when you do tilt your head.
Solution.  Don't tilt your head

There are none...

The asnwer the idiot-doctor gave you when he discovered your
astigmatism, is just wrong.

You simply have one particular eyemuscle which strains too much and
puts the eye out of shape.

You should learn how to relax that muscle and cure the astigmatism
without glasses.

There is no other answer possible.

The glasses of your idiot-doctor are just injurious things you'd be
better to trash quickly never to be put on again.

You may have noticed that once your eyes "get accustomed", when you
leav off the glasses, vision is MUCH poorer than before.

You may also be able to notice that if you stay away from your glasses
for few days, preferably staying in the open light of the sun, you
will regain a measure of good eyesight without glasses.

Now these things are real and you can test them very easily if you
want.

How these pompous professionals here can avoid to discuss these simple
truths, is really insulting.