I assume you mean ‘adverse possession’. Eminent domain, or as it is known in Australia - compulsory acquisition, refers to the process where the government resumes land under a legal right of acquisition. Private parties cannot compulsorily acquire.
My understanding of adverse possession in Tasmania is that the person must have been in possession and control of the property they’re seeking to acquire by adverse possession for a continuous period of 12 years. I’d be getting in there and forcing the issue. The longer they’re in control, the easier it will be for them to make their claim. If you’ve inherited the property and it is registered in your name, then you have the upper hand. It will be them that has to prove otherwise.