"a block cipher is a deterministic algorithm operating on fixed-length groups of bits, called blocks, with an unvarying transformation that is specified by a symmetric key. - Wikipedia "
But with a native tweak support inside a block cipher, one can achieve "varying" transformation with same symmetric key but different tweak. i.e probabilistic encryption without changing the key or using the block cipher in some mode .
Now is a block cipher with native tweak support still considered a deterministic encryption ? The only determinism being the length of the output (that is same as length of the input).