How close to plumb to deck posts need to be?
Ok Jay, here it comes!  It is important to make the posts as close to plumb as possible. The closer you are to true plumb, the less stress will be exerted on your mounting fixture. In all honesty, I think the posts are a bit tall and should have been cut to flush down closer to your pad, but then I digress.

Here is a trick to help you plumb and adjust your posts quickly.  Pound a couple of pointed pieces of 2X2 or 2X4 firmly into the ground at 90 degree angles to your post.  Then take the temp support strappings and screw them into your post with a drywall screw. You can now adjust the strapping against the ground stakes until your left and right post sides are perfectly plumb. Screw the strapping into the stake, add a second screw top and bottom and you should have a very secure, perfectly plumb post.

I see in your picture you are using strings.  That is good, but if you can get your hands on a good self-leveling laser, it would make sizing the posts so easy, and give you excellent level  cross checks as you continue to add more posts to the gridwork.  Good Luck Jay