The way that HubSpot integrates emails is extremely inefficient. We have to remember to login to an Add-On everyday and be sure to have the Add-On open at all times and select the appropriate associations for that email.
The previous CRM that we used only needed you to login to your email client through their software and it would automatically upload the emails to the appropriate contact associated with that email. It would then have that email associated with any associations for that client. Simple as that; no forgetting to login and missing emails or anything like that.
Please look into how ActiveCampaigns email integration works and work towards a solution more in line with their integration.