Why is the combustor volume of a jet engine decided by altitude?
Short Answer

It is less the volume than the length which limits the maximum altitude. The cross section of the combustor is determined by the volume flow coming from the compressor and the desired flow speed in the combustor, so this dimension is given. To enable operation at lower pressure, the length of the combustor must be sufficient, so a longer combustor will have a higher volume. That is why you have read that volume determines maximum operating altitude.

Background

The factors which make ignition easier are


pressure
temperature, and
spark energy of the ignition system


Ignition is made harder by


mean fuel droplet size (bigger droplets take longer to evaporate)
flow speed in the combustor, and
higher turbulence intensity.


For combustion to take place, first the fuel droplets injected into the air stream need to evaporate. This is made easier by higher temperature and pressure, and the lower both are, the more residence time of the fuel-air mixture in the combustor is required for good combustion. Longer combustors have higher pressure losses and weigh more, so engine designers try to limit their length.

With increasing altitude, the pressure in the combustor drops because the compressor will simply lift the pressure at it's inlet by a given multiple. Therefore, combustor pressure drops in sync with ambient pressure, and the required length for sufficient combustion goes up.