This is a hard one and will ultimately need a FAQ to clarify things.
For me I think the answer comes in the fact that it is a purchased upgrade. If you purchased a warscythes for each lord would each lord count his attacks using the warscythe? Yes. If you purchased a sempiternal weave for each lord would each one make his saves using a 2+ armor save? Yes, and so on and so forth.
If you purchased 5 mindshackle scarab upgrades (one for each) then I'd say you get to use that upgrade as long as the requirements are met. In this case, as long as all 5 lords are in base to base contact with their victim.
At the start of the Assault phase, after assault moves have been made, but before any blows are struck, randomly select an enemy model in base contact with the bearer of the mindshackle scarabs.
If that is the case, then I think each lord should get a chance to use his MS's just as he would get to use his warscythe or 2+ armor save, etc. You paid the points for that upgrade, why (like the other upgrades mentioned) would you not be able to use them if the requirements to do so were met?
If that means an MC or IC running around by himself has to take 5 tests and suffer the results of any failures (i.e. multiple D3 hits on himself), so be it.
I see the "randomly select an enemy model in base contact with the bearer of the MS's," as describing what to do if your model is in base to base with more than one model, rather than a requirement for the wargear to be used.