That's pretty close to correct. Basically, the Company drafts a stock plan requesting X amount of shares as a pool to grant. This plan has to be filed with the proxy and approved by a majority of stockholders. If approved, Tesla can grant up to that amount of shares to employees, but no more. If they want to grant more, they must come back to shareholders with another request for more shares and a majority must approve, otherwise they can't issue more shares to employees.
One key point is that forfeited shares (99% of the time) are permitted to come back into the plan. So, you'll see tons of grants and expenses, but many of these get reversed out when people terminate before the grant is vested. Tesla grants deep into its workforce, it's a very high turnover company and just about everyone is leaving behind equity when they quit/get fired, so the grant figures you are seeing greatly overstate what's actually going out to employees.
Thus, you'll typically see companies come back to seek stock plan approval (often requesting more shares) about every 5 years (though that's mainly for Code Section 162(m) purposes, I won't get into that unless you want me to).
You can see all past share approvals on Form S-8 in EDGAR if you want to see exactly what has been authorized for grant in the past. Each stock plan share pool has to be registered with the SEC, there's a filing fee, a prospectus has to be drafted for participants, etc. There's nothing being hidden and you won't wake up one day and find that employee grants greatly diluted the stock or something.
