No, it does not crash/fall.
The TarrasqueDDI's aura is:
Earthbinding aura 40; any flying creature in the aura has its fly speed reduced to 1 and maximum altitude reduced to 20 feet (putting it within the tarrasque’s reach). Any creature above this altitude at the end of its turn falls to an altitude of 20 [feet]
So, the aura imposes an altitude limit, but at the end of the flying creature's turn, the Tarrasque gravity field pulls it down in a harmless way. The aura text supersedes the effect of a lowered altitude limit (specific beats general).
Altitude limitDDI If a creature has a specified altitude limit, the creature crashes at the end of its turn if it is flying higher than that limit. See also fly speed.
If the Tarrasque moves closer to a creature flying 30 squares above ground, finds it flying speed instantly reduced to 1 (altitude limit 4), but does not move from the spot it currently occupies. When the flying creature's turn starts, its altitude is still unaffected. However, when its turn ends, the creature falls (harmlessly) to an altitude of 4 squares.
Note that without the last sentence in the Earthbinding wording, at the end of its turn the creature would have fallen (term previously known as crashed) to the ground because of its new altitude limit.
Note also that the Tarrasque is a Gargantuan creature and its space is a cube 4x4x4 squares. The aura range must be accounted from the sides of the cube, so the Earthbinding aura actually ends up affecting creatures up to 44 squares.
If you manage to move out of the aura's range before the end of your turn, then your fly speed and altitude limit return to their normal values.
The aura states that the flying creature falls to an altitude of 4 squares so it is not a forced movement (unlike a pull), however it does not provoke opportunity attacks.