If there are two competing blocks with two different timestamps at the end of the retarget period you end up with two sub-chains, each with different difficulty. They have to converge globally to the one longest chain.
This convergence is slower than the normal "orphan block/branch/sub-chain" convergence in the middle of the retarget period.
gmaxwell wrote several detailed posts about the issue, search his past posts for the word "convergence" and its variants.
thankyou very much. I will do that search.