It's normal for any wood grain to lift when its wet. It's one way of finding any loose ends of wood fibres. As Woks says, a light sand will remove them. You can't really prevent it from happening at all. Your initial stains need to be quite wet to really soak into the wood. You then either need to carry on with wet stains and be prepared to sand down lightly between stains (once the wood is dry), or then go with a dryer stain and apply more coats, and then maybe just sand down once at the end of the process.