In the game you can do it whenever you want but if you are looking to keep it like RL you would do it before you seed. We don't deal with slurry but we spread our manure in the fall and work it in, sometimes depending on what crop will be planted, we spread it, allow it to dry out for a bit, hit it with the harrows a few times to break it up and spread it evenly and the seed directly into it in the spring. For the game the most realistic would be spread it, cultivate or plow and then seed.
With manure and slurry it's not so much that you will burn the crops because they aren't as potent as strait nitrogen fertilizer IRL. The problem with manure would be that you would smother the crops and all the seed wouldn't be able to emerge through in places. With slurry it would possibly drown out the seed or plants and I think it should be worked into the soil to get the full benefit from it, otherwise a lot of the nutrients might evaporate as it started to dry out. Plus the slurry tankers are heavy and have big tires so there could be compaction issues as well.