It is done carefully. Lots of other rotating machinery has the same problem, and whole systems exist just to deal with it.
For example, jet engines are usually smaller, but also usually spin much faster. Balancing a jet engine is something that gets lots of attention at manufacturing, and again any time when it is put back together after having been sufficiently disassembled. I have worked on metrology systems designed to measure a few µm non-roundness of circular parts a meter or more in diameter. Large maintenance facilities have such systems, in addition to the manufacturers.
One method of balancing I saw used a stackup of multiple "plates". These plates were ring-like structures that would be part of the spinning system. No plate could be manufactured exactly right. The metrology system would accurately measure the asymmetries of each plate, then calculate what orientation the multiple plates have to be mounted together to make one larger object that was balanced to high precision.
There are also other techniques, like build it best you can, then balance afterwards. Actually in practise multiple techniques are employed, with final assembly balancing always one of them. This works a lot like dynamic balancing of tires. The turbine is spun slowly, and the vibrations measured synchronous to the rotations. From that a computer system calculates how much weight to add or remove where.
The most common scheme I've seen is drilling holes or indentations in a certain area of metal left available for that purpose. The computer will tell you where to drill and what diameter based on the analysis of the vibrations. In another case we has a electronic product that spun as part of its normal operation. In this case we left a few thru-hole solder pads at different angles from the shaft. The vibration analyzer then suggested which pads to fill in with solder, which was done manually by a technician in this case.
This overall process of measure and adjust is repeated until the vibrations are below some specified level. Despite the best measurements and algorithms, any one adjustment doesn't ever seem to null out the vibrations quite as much as it should in theory.