I’m going to guess that (as per the Things docs), that you are using an actin that is not allowing you to use the right authentication token for every one of your devices. From your description, I think(?), you are okay on the Mac, and iOS, but enabling it to run on your iPad results in it not working on you iOS device. In fact from what I understand of the Things docs I just looked at (I’m not a Things user), I think the authorisation token might actually be for the device rather than the OS.
I addressed exactly this sort of issue in the support for Bear I added to my library of code for Drafts. It may be that whatever action you happen to be using could be modified to accommodate that.
The alternative would be to have multiple actions that are the same, but perhaps have a different credential reference based on what device you choose to run it on.
So the former would figure out which authorisation token to use, the latter you would effectively be manually instructing it which to use.
Can you provide a link to your Things action so we could take a look at what sort of modification could be made?