Sounds like you may have Z. rehmannii. In the cut flower industry they're often referred to as "mini callas". The foliage is more elongated and doesn't have the arrowhead shape of large callas (Z. aethiopica is the large white calla most often seen). Blooming sized tubers are typically larger than peas, so it may be a year or so before you see blooms (I'm not aware of any smaller or truly "miniature" varieties on the market).
I've often found self set seedlings from mine that sound much like you describe.
