Complexity for merging 3 sorted arrays using this specific algorithtm
Assuming that you're using some random-access model of computation (i.e., not an ordinary Turing machine) and that comparisons can be done in constant time, the algorithm you describe is linear. Each element of the final array is produced by comparing at most three elements of the original arrays, so each element of the output is produced in constant time.

Perhaps you misunderstood the question and they were actually asking about something else? Perhaps they mis-stated their question and they were trying to ask about the complexity of three-way mergesort (sorting an array by splitting into three parts, recursively sorting the parts, then merging them)? Perhaps they were just wrong.