There is a custom to keep the restrictions of the "nine days" throughout the night after the ninth of Av (until midday on the tenth). When Tisha B'av falls out on Shabbat, which causes the fast to be postponed to the tenth, the prohibitions on wine and meat remain in force for that night (only), but (as mentioned here) the other prohibitions do not apply immediately following the fast.
However, the Kinnot that I used this year states that all the restrictions apply on this night.
Is there any source for this view? If so, what is their reasoning?