I wouldn't recommend keeping the bulbs in the refrigerator.* From this site.
"Tuberoses may be grown outdoors in warm climates. They flourish in sunlit places and bloom in late summer. After the last frost, plant the tuberoses in a sunny spot, beneath a couple of inches of soil and approximately a foot apart. Fertilize and water regularly. If you pot and grow tuberose indoors, keep at a temperature of 75 degrees Fahrenheit. Potted bulbs take about four to five months to bloom. Tuberose is not a hardy plant, and if it is started early inside then planted into the garden when the risk of frost is past. Tuberoses thrive in the sunshine and prefer well-drained soil. The aromatic flowers can be cut but the water must be changed daily. The plants grow two to three feet high and different bulbs bloom at different times. The tubers are planted with the top of the tuber exposed. Tubers are dug and stored in sand or peat at a temperature of 60 degrees. Remove offsets at planting time but these take more than a year to bloom."
When weeding, the best way to make sure you are removing a weed and not a valuable plant is to pull on it. If it comes out of the ground easily, it is a valuable plant.