Inigo is definitely following. He's smart enough to not give Taiki a huge obvious lead, but instead he's making sure to stick at the other's side, keeping up at Taiki's pace so they'll arrive at the same time.

And when they do, Inigo just unelegantly drops all of the buckets and shovels in his arms onto the sand before dropping to his knees next to them.

(He may seem a little sweaty, as overdressed as he is for a beach setting..)

"Phew!" He grabs one of the buckets, smiling up at Taiki. "So are you supposed to fill these with sand?"