I can confirm the same was happening to me.
Here's my opera info:
Version: 39.0.2256.48
Update stream: Stable
System: Mac OS X 10.11.6 64-bit

What I did that made the difference was to disable the "Protect me from malicious sites" option on "Privacy & security" preferences. After disabling it, opening tinyurl worked like a charm.

Hope you guys can fix this as this is a great browser, but that behaviour will prevent adoption

Filipe