Solanum is the tsundere genus - half of the species want to feed you, the other half to kill you.

On a more serious note:

The researchers found that each ancestral parent contained one key gene that—when combined—allowed tubers to grow. Tomatoes contributed the SP6A gene, which acts like a master switch to begin tuber formation. And from the Etuberosum side, another gene called IT1 controls the growth of stems that become tubers.

I did some websearch to check what the SP6A gene does in tomatoes, apparently the SP stands for self-pruning; it probably tells the plant to stop growing an appendage. I couldn’t find much info on the IT1 gene from Solanum etuberosum, but if I had to guess it tells the plant to dump carbs in the rhizomes.

If that’s correct, IT1 makes the plant keep pumping carbs into rhizomes for further growth, then SP6A says the growth is over, the carbs accumulate and you get a tuber.