My feelings agree with yours. Merriam-Webster has
instinctually under the entry for
instinct, but without a separate definition. The OED does not have an entry for
instinctually, but going off of the entry for
instinctual, I'd say that it refers more generally to something having to do with instincts while
instinctively is usually used to mean something arising from instinct. Here's what the OED says about
instinctively:
In an instinctive manner; by instinct; by some innate prompting; without conscious thought or purpose.
and
instinctual:
Of or pertaining to, involving or depending upon, instinct.