The red Rule 5 icon means that he will be exposed in this season's Rule 5 Draft because he has at least 4 years of pro experience, is not on the 40-man roster and is not signed beyond this season.
The green Rule 5 icon means he is a Rule 5 pick this season and must remain on the team's big league squad or be offered back to his original team. You have until spring training to add this player to your big league team or else he'll be automatically offered back to his original franchise. If it's after spring training and he's been acquired via waiver claim or trade, you have 3 days (72 hours) to assign him to your big league team or else he'll be automatically offered back to his original franchise.
The blue Rule 5 icon means that he is a Rule 5 pick and has been sent back to the original franchise during the offer back process where they have the option to accept or decline the return.