It's been a predictable daily event for years now. I can't count the number of times I've had to race or bump fees to beat their morning flood of withdrawals. They are a plague on the network.
This is predictable if you frequently use bitcoin, but not as much if you are a more casual user.
Indeed, it's a great example of the difficulties underlying in-wallet fee estimation. BitMEX has the power to drastically alter the fee market, and it's impossible to anticipate exactly how large their load will be or what fees they will use.
In regards to casual users, the only immediate solution is to encourage the use of RBF, and wallets that support it.
The community putting pressure on BitMEX to at least implement broadcast delays could also help. Dumping all those transactions in a 2-minute window everyday is just horribly inefficient.