Contact synchronization (with Google accounts) is handled by Android / Google not AquaMail.
For this to work, the account has to be added into the phone's system setting as such (a Google account).
Once this is done, you can go back into system settings -> accounts -> Google -> tap the account to show the list of all the various things which are set up to sync with Google's cloud (such as: Play TV, Magazines, Google Fit, etc. etc. etc.) and turn off "Email" keeping only "Contacts".