What assurances do we have that we can safely store the DCR on evolution.dcrstats.com without risk of getting funds stolen, hacked, etc?
as usual, in this world, the words & reputation of the founders/developers of the project

so basically - none
Correct, but there is one more feature for security. All funds locked in tickets (PoS mining), so even if hacker get access to the server, he cannot steal any funds or he can get very little spendable amount (like 1-2% of total).
Thanks for the clarification,
I mainly addressed the first part "...stolen", take a notice on the signature: "...Victim of the... MtGox Heist"
anyway, Decred Evolution is a good service so far and potentially a great platform for the development and adding new features to the Decred ecosystem,
wish it was ready at the time of the airdrop
