With the landing of bug 783282 you are not able anymore to turn a normal tab into an app tab by just dragging it into the app tab area.
This was intentionally done as part of bug 783282. There's bug 579629 as a possible long-term solution, but it's unclear how exactly this would be implemented. Suggesting wontfix for this particular regression. The primary way to pin a tab has always been the context menu.
It has always been considered as a followup to tab manipulation. The animation should be there when you pin the tab via the context menu or tab dragging.
According to comment 1 this doesn't seem like a tracking bug as it will likely be resolved invalid or wontfix. Please renominate if that changes.
*** Bug 832631 has been marked as a duplicate of this bug. ***
this is now possible between different windows - see bug 886154
*** Bug 863667 has been marked as a duplicate of this bug. ***