Exactly, your service doesn't have an option built in for setting delayed start. It's more a feature request, there is no "cause" to fix, just add one of the service start options of "delayed start", for instance if I were to set one of my services I've written I would do something like this:
SCMHandle := OpenSCManager(nil, nil, SC_MANAGER_ALL_ACCESS);
if SCMHandle <> 0 then
begin
ServiceHandle := OpenService(SCMHandle, PChar('MyService'), SERVICE_CHANGE_CONFIG);
if ServiceHandle <> 0 then
begin
// Set the startup type to Automatic (Delayed Start)
DelayedStartInfo.fDelayedAutoStart := True;
ChangeServiceConfig2(ServiceHandle, SERVICE_CONFIG_DELAYED_AUTO_START_INFO, @DelayedStartInfo)
end;
end;