General help

AFAIK, the process should be automatic, or it was made automatic when the course using the activities was set up.  The idea of certificates was only introduced in v1.6.x. I am pretty sure the process was raw, so conditional automaticity was not a feature, but, from memory, became one in the v1.9.x+ that could be connected a range of activities. For this reason, I don't think there was ever developed a way for you to check who had downloaded certificates or not, at least not in v1.9.x.  

I also recall there was a help button at the bottom of the page available that linked you to a set of instructions to help guide you through the setup and printing options.  I am sure there was also a block you could add to check the conditional completion process, but I don't believe that is available any more. In the end, it is likely the only real option for you may be to send everyone in the course an email to remind them to download their certificates when they have successfully completed the required activities. 

Aside: The real problem for you is that v1.9.x is now close to 3 years out of date, so there is no development work on  it, no further security patches and the skill base previously developed to deal with this sort of issue has been greatly eroded. Sorry that this has taken so long for you get some attention, but this is why. You really need to upgrade to v2.2 then to v2.4 and then v2.6 and then v2.9 as all of this is really setup clearly. I know this is not always possible, but your organization really needs to consider updating.