When someone books a meeting with you, they always get a booking confirmation from NeetoCal. Depending on which calendar you have connected, they may also get a separate calendar invitation sent by that calendar provider. That second email is why some customers see two emails for a single booking.
The booking confirmation from NeetoCal
NeetoCal sends this on every booking. It confirms the meeting is scheduled and includes the date, time, and the answers the customer gave on your booking form.
The calendar invitation from your calendar provider
When you have a calendar connected, NeetoCal adds the meeting to your calendar and adds the customer to that event as a guest. Some calendar providers then email their guests directly, and that email arrives alongside the NeetoCal confirmation. Whether it happens depends on which calendar you use.
Google Calendar
Customers receive two emails: NeetoCal booking confirmation and a calendar invitation from Google. Google also emails them when a meeting is rescheduled or cancelled.
NeetoCal does not include its own calendar invitation in the confirmation email when Google Calendar is connected, since Google's invitation already carries the event. There is currently no way to stop Google from sending its invitation.
Outlook Calendar
Customers receive two emails: NeetoCal booking confirmation and a calendar invitation from Outlook. Outlook also emails them when a meeting is rescheduled or cancelled.
Outlook always emails the people invited to an event, and Microsoft does not give apps a way to switch that off, so NeetoCal cannot stop it. Microsoft has confirmed this in its own documentation:
iCloud Calendar
Customers receive one email: the NeetoCal booking confirmation. iCloud does not email guests, so NeetoCal includes its own calendar invitation in the confirmation instead.