It's correct because 'actuality' is a noun. For instance, you can't say 'in actually', because actually is an entirely different part of speech. Thus, while the meaning of 'in actuality' and 'actually' might, in interpretation, have the same value or meaning to you, they aren't at all the same grammatically. I'll use an example you're probably more familiar with.

'In actuality' is the equivalent of saying 'in reality'. In fact, that's what 'actuality' means: 'in reality, in existence'. That phrase doesn't bother you, does it? They're both stressing the fact that 'this is how it really is'. Actuality becomes 'actually' the same way 'reality' becomes 'really'. It's really due to preference. 'In realty' and 'in actuality' are a more emphasized form of 'really' and 'actually'.

It's kind of like the concept of wordiness: using more words to emphasize a certain point---more than necessary---where some people might prefer to use a more brief and direct form.

'In actuality' is correct. You shouldn't let it annoy you, just change the wording in your head to 'in reality' or 'actually' if it bothers you.