Hey Gerard. Yes, we are using classic. I just switched an account over to lightening to take a look but same results. People that are scoring for web activity are showing no web activity in the tab.
Is this for both leads and contacts? We're having a similar issue with our Marketo-Salesforce sync in that our leads are getting the data, but once the lead is converted, the contact isn't maintaining that respective lead data. It's as if Marketo is moving too fast for Salesforce conversion so once the lead is converted to a contact, the Last Interesting Moment data is blank for a minute, and Marketo pulls in the blank data, and then syncs with Salesforce again, thus keeping the Last Interesting Moment fields blank.
You can upgrade here: https://appexchange.salesforce.com/listingDetail?listingId=a0N30000001SVZmEAO
Instructions for the upgrade process are noted here: https://docs.marketo.com/display/public/DOCS/Upgrade+Marketo+Sales+Insight+for+Salesforce1