What tessellation shader are you using on ios that is currently working? Can you share it with us for further investigation, together with the ASE shader? You can do so via firstname.lastname@example.org if you'd rather share it privately.
The tessellation technique used in ASE is the same as Unity's so, if Unity's tessellation shaders are working in ios, so should ASE.
The sample I've sent is a Unity Standard shader and, since we use Unity's Tessellation on ASE, if it doesn't work it means that there is an issue on Unity side regarding support on iOS.
If this sample works, it means that there is in fact an issue on our side, and we will proceed to investigate it.
On a side note, I did notice that they mention at the end of the manual page I've shared that they've added support for Tessellation for Metal added in 2018.1, but this might not guarantee that it works on all devices.
It seems that Unity's tessellation technique still has some issues, unfortunately there's nothing that we can do on our side in regards to this. As such, I'd suggest that you get in touch with Unity to report the issue you're having while also providing details such as Unity version and target device.
We'll also be keeping an eye out for any possible fixes on Unity's side regarding tessellation on iOS/Metal issues.
Apologies for the inconvenience, please don't hesitate to get back in touch if you come across any other issues.