I also noticed this when I went to start a franchise with the conference championship as my starting weekend. The draft picks are so messed up, no one has the correct picks. Last night I messed around with it though and if you start during the wild card weekend teams have their correct picks. If your planning on taking on a rebuilding team that should work for you, if you care about the correct playoff results you could just give a force win to the correct teams each round. If you start in the divisional round or conference championship though the draft picks are messed up. I really don't know how they missed this issue.
The other thing I noticed is if you start a franchise during week 17 or actually I believe during any part of the season then Le'Veon Bell hits free agency but if you start one during any point in the playoffs the Steelers always franchise tag him. I guess it depends on whether you care about Bell hitting free agency. In real life they probably won't franchise him because of the cost, it is possible they use the transition tag on him but I think ultimately they let him walk to free agency. If he does go to free agency though be aware that almost every time the Rams will try and sign him and about 70% of the time they do sign him which is stupid and I usually end up restarting if that happens. It's annoying that there is even anger kind of logic in the game that has the Rams signing Bell.