MobileCoin uses a combination of two other private coins, Monero and Zcash. There are no addresses on the MobileCoins's blockchain to be correlated. Didn't it cross your mind that a private messenger would probably use a private cryptocurrency?
MobileCoin does not use any Zcash technology. It is Monero + stellar consensus protocol.
...and SGX, which is very interesting and a choice worthy of scrutiny imo.
With a "private" crypto-currency you're still making a bet that there's no exploit. Roping payments into a message app increases the attack surface for both.
Monero's primatives are pretty well researched [0]. Of course there is always the chance of bugs in the implimentation but it looks MobileCoin's crypto primatives library has at least been audited [1].