The minerals in the ocean precipitated as they became more concentrated during the formation of the iceball. The carbonates referenced in the article are a part of this. During the snowball period, volcanos at the edges of the plate breakup introduced more minerals which mixed with those picked up in the erosion by the fresh water. There were a lot of things happening at the over the warming. Today, you can find the minerals precipitated due to the initial freezing in some lateritic ores.
What precipitates eventually redissolves. Otherwise there would be no saltwater.