At a quick glance, it seems that a simple HDMI splitter might be the solution to your query?

I am assuming the projectors are in a proximity to the laptop and no SDI or similar is needed?

The Atem Mini will only loop the signal in/out. The units normally have 4 inputs and one output. If you are using the atem, then put the HDMI splitter in line from the output of the atem. 

If you have another laptop or media player, then the atem might be handy. Otherwise it might not help etc.

Your cheapo splitter is normally 4:1 (4 outputs to 1 input). Obviously, if you are looking for more than 4 projectors, then you would need a larger model or a second unit. I would keep the HDMI runs to as low a measurement as practical. 

You can pick up 4:1 4k HDMI splitters for less than €100. 

There may be better recommendations of brands here from others but you could pick up a cheap splitter/decent quality cables and trial it without much cost.

The set up should be plug and play here.

Link to sample 4:1 splitter, HERE

eamon