Ed and Gayle correctly pointed out that short day plants (those that bloom in the spring or the fall) can sometimes do both. The asters probably experienced some transplant shock in the fall, which would have suspended floral bud development. This phenomenon could also be due to mild winter conditions (as Ed and Gayle also mentioned), which could have spared flower buds normally killed by freezing temperatures.
In any case, as spring daylengths approached those found in the fall, flower development continued and voila! Asters in the spring! Likewise, there are a number of spring bloomers that sometimes have a second (usually reduced) floral display in the fall.
Thanks again to Ginny for sharing her photographs and information!