The primal skills actually say the cooldown sharing is between Feather Rain/Eruption, Mountain Buster/Shock Strike, and Glass Dance/Veil of the Whorl, which are 30, 60, and 90 second cooldowns respectively. Everything else says "Does not share a recast time with other blue magic skills".
I'm inclined to believe that means you'll be able to pick between those ones, since BLU's rotation would be extremely stale otherwise.