Hopefully you will all get along & it will not matter. If things get really crazy, you can get a survey done & then you will know exactly where your property is. Good luck.
I've attached a link to the Whatcom County Assessorâ€™s office Parcel Viewer. You can type in the address or parcel number of your property and get an Arial view of your property and the surrounding ones as well. This would be a start.
Taking the agent or the neighborâ€™s word is equally risky. People may think a piece of property belongs to them because they've used it, but this isn't ownership. Agents may repeat something they've been told, but it may not be accurate. Checking it out for yourself is always advisable if the issue is important.
If the adjoining property is shared, I doubt it will be labeled as a compost site, but may belong to the neighborhood association and fallen into that use through agreement or default.
Start with the link if it isn't clear, check with a Title Company. As others have said the legal description may include a separate parcel is joined to this one as community or jointly owned by the neighbors. I hope this was helpful.
Is there a Home Owners Association? If so maybe check there. Also maybe check the CC&R's if there are any.
It sounds like you purchased the home already. If you still have it, check the disclosure and see what it says in the disclosure about this.
You might also ask the neighbor to show you written documents he as showing the property is his.