Changing the download directory requires a simple change to the Downloads setting under Transfers in the preferences interface. Below are the steps to make this change.
Bring up the Aspera Connect preferences page
To open the Connect preferences page, select the cog icon in the bottom left corner of the Connect plugin(displayed above on the left side). Alternatively, in Windows, the Connect preferences can be displayed by right clicking the Connect icon and selecting Preferences(displayed above on the right side).
In Mac OS, you can open the Connect Preferences by bringing down the Connect menu in the taskbar and selecting Preferences... Alternatively, you can hit the command key in combination with the comma key(,) when the Connect plugin is selected.
Navigate to the Transfers tab and edit the Downloads preference
Select the Tranfers tab to bring up the Tranfers preferences. In this tab, you can view and edit the Downloads preference. Selecting Save downloaded files to: will allow you to browse and choose a directory where you wish to download files to. Selecting Always ask me where to save downloaded files will make it so when downloading a file you are prompted to select a directory. This completes the process of changing the download location.