The Bluefin gateway will automatically notify your givers when they make a donation. But without the proper settings in the gateway settings in your Bluefin Payconex account, you may be sending them too many emails or not enough.
Go to Settings > Manage Settings and scroll down to Notification Rules
Here are the recommended settings:
Note: Setting Send Customer Receipt to "No" will still deliver "one-time" transaction receipts and will prevent the end-user from getting notified during authorizations, which is ideal.