Both Aha! and Github Issues have the capability to assign items to an owner - but there is no synchronization between Aha! and Github Issues.
Ideally - within the GitHub integrations section - you could assign a Github name to every user - so when a feature, requirement, release is assigned to that person - and you send it to Github Issues - the right resource receives it.
This eliminates the need for a project manager/ corresponding resource to comb through issues and assign them to the right person, as it has already been done in Aha!