That is precisely correct. If your vacation package includes any version of the Dining Plan, you shouldn't try to upgrade your ticket to an AP until after all dining credits have been used. Doing so will void all remaining dining credits on your reservation and it's a huge problem to try and get them fixed (if it's even possible).
If you just have a regular package, Guest Relations should be able to "extract" the ticket off of your room key and use it toward the AP right away.
If you upgrade on the final day of your trip, the AP will be back-dated with a start date of the first day you used the ticket. If you do it right away, the start date will be that date, even if you haven't used the ticket yet.
And as someone else said, if your ticket has the Water Parks & More option and you've *used* any of those options, you will be forced to upgrade to a Premium Annual Pass. I'm 90% sure that upgrading the ticket must be done within the 14-day window from its first use, even if the No Expiration option was paid for. (And this applies to all ticket upgrades... After 14 days the unused days don't expire, but the ticket is locked into what it has for features and days at that point and can't be changed)
Lastly, the AP upgrade must be done at a theme park or Downtown Disney Guest Relations window (and possibly at any ticket window too, but I'd feel better going to Guest Relations). It cannot be done at your resort, as resort CMs cannot sell Annual Passes.
-Rob