The fountain pen leak at high altitudes is because of low air pressure. The ink inside the fountain pen has high pressure compared to the low atmospheric pressure at high altitudes. So the ink flows out of the pen.
when the ink is filled inside the pen at normal sea level,
it is filled at a certain atmospheric pressure.
But
when we go to a higher altitude
and
the pressure increases
and
the air column exerts a pressure on the ink in the tube of the pen,
as a result of which the ink is pushed upwards.
The pressure of atmosphere becomes so extreme at a point that the pen ink starts leaking
The air in the ink reservoir is at atmospheric pressure. As the surrounding pressure drops the air in the reservoir expands and pushes ink out.