So how does the IRS treat vesting shares of a company like Uber? I doubt people get to make their own determination of the vest value, but I don't really know how the price is determined exactly.
Vesting _options_ aren't taxed until you exercise them.
When you exercise them, the company's most recent valuation will include a value for the common stock you purchased, and you can get hit by AMT on the value increase from the strike price to the current value.
Note: I am not a tax expert and my memory is imperfect.