If the tool is set to run automatically, then follow-ups will most likely be sent, the day after an invite to connect is approved.
If you are managing the tool manually, then the follow-ups will be sent:
a) If the 'send followups' option is turned 'on' within your campaign settings.
b) The followups will be sent only to people that have accepted your invitation to connect.
It's also important to note that while the 'followups' process is running, Growth-X monitors your 'connections' tab to analyze who your new connections are (which were invited to connect by the tool).
This is how the app knows who to send follow-ups to.