Are you sure? I do remember now that if someone accepts a qualifying offer contract you can't trade them without consent until June 15th, but I don't recall anything about signed FAs.
And there I found it. Thanks for educating me. I didn't know this existed.
Edit.
5. An Article XX-B MLB free-agent who signs a Major League contract after 11:59 PM (Eastern) on the 5th day after the final game of the World Series has an automatic "no trade" right through June 15th. The player can waive this right, but if he does he can be traded only for cash and/or player contracts with a maximum aggregate value of $50,000. Note that an Article XX-B MLB free-agent who signs a minor league contract after 11:59 PM (Eastern) on the 5th day after the final game of the World Series does NOT receive an automatic "no trade" right, even if the player is later added to the club's MLB Reserve List (40-man roster).