Please do some research before posting:
Exodus will automatically start the unstake process for all your EOS tokens when you access it for the first time using Exodus. The advanced drawer item called Refund shows you the number of EOS tokens that are being unstaked along with a countdown timer which tells you how long it will take for the unstaking to complete
..
If you want to stake your EOS post the default unstake inside Exodus, you can do so using other wallets which support staking.
From https://support.exodus.io/article/892-eos-advanced-menu-options (under "Refund").
The team from @exodus is not creating any transactions and no private key is compromised, what you described is the default behaviour of the wallet when you start it for the first time. The unstake process is initiated by the wallet software when you start for the first time (it's a bit redundant to say, but just to be sure: this is done from your computer).
And please don't say "Not a FUD title", when it clearly is. And again: do some research first!