There is not really a secure way to prove that it got xrayed unless you recorded them so there is nothing that can be done about this really, sorry.
(It's possible that they saw your nametag underground, set home and then just came back when you were offline)
In this day and age, unclaimed bases are very likely to get xrayed. The map is so small it takes no effort at all to find interesting things underground. Seeing as XRaying is not targetted by the Desteria Anticheat, and it's something people do on their own, they're unlikely to get recorded/caught doing it as well. If you want to have a base that's safe, you claim it and protect it. That's just how it works these days.