Hassio is available on many machine types/SBCs and it takes time to render each image per board after Home Assistant itself has been updated.
stable: https://s3.amazonaws.com/hassio-version/stable.json
beta: https://s3.amazonaws.com/hassio-version/beta.json
When the version is visible there, the Supervior will find it and present an "update available" card on the Hass.io dashboard.
You can force Supervisor to check by reloading the Supervisor at Hassio>System>Hass.io supervisor in the UI, or hassio su reload
in the CLI.
The command to install a specific version of Home Assistant from the Hassio cli is hassio ha update --version=0.XX.XX
substituting X for the version number you want.
You can use this to effectively bypass the self check that the supervisor makes. If the version you are looking for is available at https://hub.docker.com/u/homeassistant for your machine type under "tags", then you can specify that version.
For example, for a pi3 running 32bit you would check: https://hub.docker.com/r/homeassistant/raspberrypi3-homeassistant/tags
Or for a generic linux install: https://hub.docker.com/r/homeassistant/qemux86-64-homeassistant/tags