Sorry, sloppy post. It does have both, but full local access requires a bit more work and is not ‘official’.
Out of the box, programmed schedules are saved on the local controller. Thus if there is cloud outage, these continue to work correctly.
API access officially requires the cloud. However, some enterprising individuals have reverse engineered the radio communications protocols that Evohome uses between the controller and the individual devices (in fact, I recall seeing one one of them, Danny @dty, in the openHAB forums), and written firmware for an arduino to sit in the middle. Over in Domoticz, they have written a two-way interface that both listens to and sends commands to Evohome.
Using their work, and Danny’s firmware, I put together a simple python based ‘listener’ that directly listens to Evohome messages and posts them to an mqtt broker (GitHub - smar000/evoGateway: Python script for listening in and responding to evohome heating control radio messages). This then updates my openHAB, Grafana charts etc.
What I haven’t yet done is add the additional functions to send messages to the controller/devices, though this is there in the Domoticz repo, and hopefully shouldn’t be too difficult. I haven’t had a need to do this and have been using the cloud API for sending instructions, but may get round to it one day if time permits and the need arises. As of date, the Evohome 2 binding does not use the local arduino based ‘listener’, though the binding author over in the thread expressed interest in doing so at some stage. I don’t know if he has progressed this side of things as yet.
Some notes/photos on the arduino setup: Evohome binding 2.0 - #154 by smar
Edit: I forgot to mention that ready built arduinos with the radio board, both soldered onto a proper PCB are available on Ebay.