It is possible that the plugs are grown from cuttings, rather than tubers. (or that they are cloned from cells) I believe (and begonias are not something I know much about) that it may be pretty easy to grow begonias from cuttings; or using the leaf method.
When your plants are growing well in the summer, you could try this; take a leaf, make a few incisions with a sharp knife, lay it on some moist gritty compost in a small pot, pin it down with dressmakers pins, place the pot in a clear polythene bag and leave for a week or two. In principle you should get several of the cuts in the leaves forming roots. And therefore...plants. If you have somewhere to keep them through the winter; a conservatory or frost free greenhouse or a south facing windowsill; you will have your plants for next summer; free. Though, one neighbour I believe digs up the tubers and keeps them somewhere dry and above freezing to plant in her troughs the following year.