Unfortunately, we can't guarantee that grommets (or any fasteners) from other sources would fit or work properly with the dies we carry. That's because our dies are custom molded to exact specifications of the grommets we sell, which is why our system yields consistently perfect results. (The same would be true with any professional press system.)
Grommets are generally measured by their internal hole diameter. But that's just one of many dimensions. Height, width, and thickness are some other specifications that need to be considered.
And unfortunately, there's no way to know for sure until you actually try it. For that reason, it is always recommended that fasteners, dies and presses be purchased from the same source -- to ensure compatibility.