We don't know do they have billions of money backed by Tether so I think USDT price instability will increase until they do an independent audit and publish us the results. There is no trust because we don't see billions of money in their in bank accounts.
Aside from allowing audits of their financial records, the next problem that USDT faces at the moment is the entry of new stablecoins into the market. Most of which are a lot more transparent and also some exchanges are beginning to introduce fist deposit and some trading pairs.
This means tether gradually is loosing its grip of the major stable coin.