njbb,
You are exactly right. I think we are saying similar things in a different way, but the Milb contract can cause that.
The Milb contract requires 6 full Championship seasons.
Anyone signing after the draft in June would not have that season qualify as a "full" Championship season since the MLB definition in the contract of a Championship season is April until the end of the MLB schedule.
The first full Championship season for a player drafted and signing from June 2004 would begin the following April and they are contractually bound for that 1st season and 5 more following that.