If you were not warned in advance that a cracking condition could result, the contractor was not being as responsible as we think contractors should be to consumers. Unfortunately for you, no law has been broken here. But an experienced contractor who works with ceramic tile is well aware that a substantial substrate is needed to prevent grout cracking when tile is installed over a wood floor.
In new construction when tile is used over a wood-frame floor, the strength of the floor in that area is increased and it is usually built about two inches lower than the floors that don't get tile or stone. This makes room for a two-inch-thick layer of mortar and steel rods that adds rigidity and strength.
In remodel construction, the floor is reinforced from below with extra piers and-or additional floor framing members. It is wise to add a one inch thick layer of mortar below the tile for even more strength. Unfortunately, this is expensive and usually creates a change in floor levels that is hard to get used to.
Without being there it is difficult for us to determine whether your floor is flexing or shifting laterally both can cause the condition you describe. If your contractor is right, extra supports under the house will reduce flexing. But, if your house is shifting laterally other measures may have to be taken.
We hate to tell you this, but it might be cheaper to assume that the contractor is right and add the supports. The job can probably be done for less money than it would cost to hire a geotechnical (soils) engineer to investigate.
If the condition persists once supports have been installed, contact a soils engineer.