How long does it take for the controllers to connect to the cloud after startup?

The time it will take for a controller to connect initially to the cloud is highly dependant on the firmware version of the controller. The connection times are detailed below

less than v0.6.0 - will attempt to connect to the cloud every hour.
v0.6.0 and above - will attempt to connect to the cloud every 15 minutes with a random offset.

All controllers on firmware v0.6.0 and above will attempt to connect to the cloud at startup depending on the state of the connected network, if the controller has no detectable network on startup, it will connect when networking is established.