There have been reports in the past that the Cubs will reach an agreement with a prospective draftee to give him XX dollars, plus anything they have left over after signing everyone else. it looks like this was the situation here. They might have said to him "we will give you slot plus whatever is left on the table after we sign everyone else. We estimate that will be around XX dollars, but can not be certain. Of course, this requires a lot of trust on both sides, but these teams spend literally years cultivating these kids, and have a feel for who can be trusted.
This might have been an easy one for the Cubs to use that strategy because, if he refused to sign at the last minute, they just lose the slot money and have everyone else signed. Next year they get a replacement draft slot with it's replacement slot money.