B button battle initiations also 'encourages' party members, this means you get the <3 for it: I think the formal name is "Burst Affinity".
First, it raises the character's tension ---- essentially their morale as shown by their battle portrait (they look angrier and, literally, 'fired up'). Tension affects the accuracy of attacks, the amount of damage during chain attacks, and the probability of "critical healing".
Second, it raises affinity between the characters, making it easier to do chain attacks in the future.
And a small third: Affinity can also help when creating Gems (the weapon power-up attachments). More than likely you'll be able to build a quick and budding friendship with Reyn given he's the first and longest staying party member.
So yeah, initiate those battles!