"I received a Form 3921 from that company and filed this transaction in my taxes the following year."
I really don't know what that means. I assume you made some sort of entry for AMT purposes even though there was no "spread" between what you paid and FMV? That is, the actual adjustment was $0? (The entry should have really been made in the year you exercised as it's not selling all the stock acquired via an ISO in the year of acquisitions that triggers AMT.) There's no other way to "file" a Form 3921 that I'm aware of.
"1) How do I report the income of the sale of ADS shares? Does this receive long term capital gains treatment? How does the IRS associate that I held those shares for more than 1 year (as filed in my previous year return and also disclosed in the 3921) to my ADS sale?"
This is strictly a seat of the pants answer without any sort of cite, but I don't see any problem at all, you simply report the sale of the ADS and indicate the purchase date, back before the IPO. The 4:1 ratio of "stock" to ADS seems to be nothing more than a "stock split", from your perspective. Given the time gap it sure is a long term capital gain. I would guess the IRS wouldn't even try to "associate" the sale with the Form 3921.
If the IRS ever asks about the sale, I'd bet money and give you odds that they won't, you explain things to them.
"2) What do I report as the tax basis? Since it’s 4 class A shares : 1 ADS share, is that $0.40 / share? How do I do this TurboTax?
If it takes 4 shares of stock to get one ADS then, yep, your basis is $.40 per ADS. The easiest way to "do this" in TurboTax is to simply fill in the "Cost or other basis" box on the standard "1099-B" entry form TurboTax presents to you in the interview. There's no need to show any detail when reporting a security sale. Again, if the IRS ever asks about the sale, you explain how you calculated the basis, and you're done.
