You can actually mix everything dry and fill and then wet. It makes it take longer for everything to become moistened and may involve a few waterings, but it will still happen.

What you did sounds fine though. Give it a little time and water again just to be sure and things should be good.

The two week period to let the lime react with the mix is not strictly necessary, just a nice thing to do if there is time. You won't harm your plants by not waiting 2 weeks. By waiting the 2 weeks the lime has reacted with the mix, calcium is available and the pH is in a good range. None of this is so super critical that you can't plant right away if you need to.

What to do with new plants is up to you. You can either put them directly in the mix without removing the nursery soil from the roots or you can remove it first. With small plants that will become large I generally don't bare root, but with gallon sized plants I always bare root to remove the old mix. This may result in the plant wilting for a few days as all of the hair roots are removed in this process no matter how careful you are.

If possible keep them out of direct sun/intense heat/strong wind for a week or so. Otherwise just keep well watered and accept that they may be droopy/wilty for a little while.