If you are unsure whether an email was sent from an Apsona list view, merge action, etc. the best place to start is by going to Salesforce Setup. Type in "email log" in the left hand column and go to the Email Log page. Click the button to make a request. Enter the date/time parameters that you want to see. After submitting, Salesforce will email you a link to get the results. You will get a .csv file of all incoming and outgoing emails within the time period you referenced. Look for email addresses that were in the data source for your Apsona operation. If you see them, then the email was sent. If you don't, then it wasn't.
Further context: When Apsona sends emails, what it is really doing is prepping and packaging those emails, and then it sends them to Salesforce to send. Apsona uses Salesforce's email engine to send email. As a result of this, Apsona does not have control or logging options regarding emails. That is why using the email log function in Salesforce is the best way to know if an email was sent. Note that Salesforce imposes various limits to how many emails can be sent out each day and this could affect Apsona operations as well. This article is a starting point if you want to research further.