Those pictures are leading me to a think a couple of things. First, IMO, they are no way complete in their assembly. A couple of air driven framing nails in the joint area are doing no good other than holding the outside board to the middle board. There's plenty of space there for a steel plate to be installed later. Once all the columns are plumbed, the joints could be secured with bolts all the way through the 3 members. Second, the gaps between the lower and upper members are not that bad, if all three members are secured as one unit.
When we built our posts, used treated at the bottom, SYP above ground level. We assembled them as we moved up in elevation. Piecing them together, with 4' staggered joints, getting all plumb and square, while attaching the sidewall purlins. I didn't use steel plates at the joints, but did fill the posts with 60p pole barn nails (ring shank) using an air nailer. Groups of 5 nails, shot in from both sides at 2' intervals.
The strength of a nail-laminated beam, is dependent upon securing all three members together, in a methodical pattern. Just attaching the outside members to the inside member, places all the stress on the inside member. The 60p pole barn nails we used, in some cases, extended all the way through built up posts, with the point sticking out the far member.
OP, keep an eye on the those columns. I don't believe they are in no way complete. But if the contractor wants to leave them that unsecured, I suggest having a discussion with him.
