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 LinkedIn campaign settings.
b) The follow-ups will be sent only to people who 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.