Some commentaries interpret the Beraisa to which you are referring with reference to Chol ha'Moed (in connection with which it is written), and the Gemara cites it here only in order to define 'Tzorchei Rabim'.

Others do indeed interpret it also with reference to the second half of Adar. This does not however mean that Beis Din deliberately waited until then (if it did, your question would extend to almost all the cases, since, to leave all the things listed until Adar, would not only be senseless, but would also place an impossible burden on the Batei Din at a time of year when they have other things to concentrate on). What the Tana means is that, in the event that any of the cases listed were in the process of being dealt with, they would make sure that when mid-Adar arrived, the case was completed before Rosh Chodesh Nisan.

Be'Virchas Kol Tuv

Eliezer Chrysler.