All dates and times in Channeltivity are recorded in GMT/UTC and when information from a "Date" or "DateTime" field  in Channeltivity is pushed into a "DateTime" field in HubSpot (such as the built-in Close Date property in HubSpot), HubSpot automatically converts the date and time to the timezone of the User viewing the record in HubSpot. 

For example, the custom DateTime field in Channeltivity (highlighted in red) in the below screenshot is mapped to HubSpot's built-in Close Date field, which is a DateTime property. The Channeltivity field shows July 30, 2019 2:30 AM GMT, but in HubSpot, it shows July 29, 2019, 10:30PM EDT (see second screenshot).  

Custom DateTime Field- Channeltivity 

Close Date Field- HubSpot

How can I fix this issue?

Instead of mapping Date and DateTime fields in Channeltivity to "DateTime" fields in HubSpot, we recommend you map them to custom "Date Picker" fields instead. HubSpot does not apply timezone formatting/conversion to Date Picker fields, so it will eliminate the timezone confusion for your HubSpot Users.