Found the solution to this some days ago: you need to change your System Spell checker to Heliboard.
Now the developer added it to the FAQ too:
Spell checker is not checking all languages in multilingual typing: Make sure you actually enabled HeliBoard spell checker. Usually it can be found in System Settings -> System -> Languages -> Advanced -> Spell Checker, but this may depend on Android version.
Glad that it worked out in the end. It’s a pity that different Android versions and custom ROMs have this setting in different places, I guess this is also making it impossible for the developer to put a direct link to this setting in Heliboard that would work for all users.