Use of tillage to control SDS has been extensively discussed. From the soil conservation consideration, tillage increases erosion and production cost. So it is not encouraged. If you have done tillage, it will not increase the risk for SDS risk, as it does for white mold.

Published literature over the last 20 years consistently showed a higher risk of SDS in no-till than in tilled fields. No data from peer-reviewed publications have suggested no-till can reduce SDS. SDS is more severe under no-till than other tillage practices because of cooler soil and higher soil moisture during spring in no-till fields. Tillage increases soil temperatures and reduces spring soil moisture, which reduces the risk of soybean sudden death syndrome.  Any practices that reduce soil compaction will certainly help reduce SDS.

For fields that have had both SDS and white mold in the past, use of tillage or no-till does not matter as tillage impacts the two diseases in opposite ways. If you know what disease had the higher occurrence in a particular field, you can make your decision accordingly. Because you would not be able to predict which disease is going to be prevalent next summer, the two diseases pose the same risk as they both can reduce yield significantly if an outbreak occurs.