Hello, wouldn't worry too much about the wet getting in as everything is packed so well to protect it!
We didn't have our container loaded in rain but we were snowed in at the time and the packers had to load everything whilst wading through several inches of snow from the house. They had to use a tractor to pull the small lorry they had to use up to our house (and out of a ditch) and they had to walk a mile from the main road to our house themselves. Everywhere was wet and dirty in the end but when everything was unpacked it was all fine. No damp or mould at all, just funny to see the dirty packaging on some of our items, three months later. So I wouldn't worry too much, hope it all went well! You will look back and laugh in retrospect!