In contrast to AVL trees where rotations for deletions may propagate up to the root (although having at most one (double-)rotation for insert), RB trees require a constant (at most 2 for insert, at most 3 for deletion) number of rotations. What can take logarithmically much time during deletion in an RB tree is the recoloring which may propagate up to the root, which means insert and delete have the same asymptotics for both AVL and RB trees.
(If interested, you can find an analysis of these things in this script.)
Regarding your question, at most 3K is correct (but apparently rotations are counted a little differently from the linked script).