The game will automatically start when all seven players have joined.
I have the "Civil Disorder" rule enabled. What that means is that if you miss a deadline, the DPJudge does your turn for you. Which means that during a movement phase, all of your units will do nothing. They will sit there and "hold". If you miss a retreat deadline, the judge will disband your unit! And if you miss a build deadline, then the judge will waive your build.
As you can see, it would be a good idea to not miss a deadline.
If you run into extremely urgent circumstances, like you'll be out on vacation on a deserted island for a week, then just send a broadcast press out to everyone asking for a delay for that phase. If the majority of folks don't have a problem with that, I'll gladly extend the deadline for a phase until you get back.