Right have been working with a few different groups to try and confirm what the Blue ring debuff actually does and how to counter it.
Answer...unknown its not very consistant and there is no hover over info (e.g. does not appear as a debuff on character stats).
It is anti proton damage and comes from the team member that has the debuff on them.
It does hurt.
It does not trigger if loose line of sight......this may change with todays patch as no running behind anything due to addition of plasma.
It has been hinted that the debuff will trigger regardless of what you do and is an indicator that that member of the team should move away from group.
It still triggers if team member runs off half way across room e.g. away from the rest of group so this is not best plan due to the fact it still hits group members and you then run risk of respawning borg aggro.
This info about running away from group or spreading out seems to be a red herring. While you should not always do the opposite of what a dev suggests in this case i would reccommend to ignore the info and get your whole group to stand close together in melee range of Rebecca.
Certainly this is the best tactic and you can ignore the blue debuff. You will still need some hypos but the damage is completely manageable.
We have been running with one sci, one eng and 3 tacticals. Sci is doing some form of area healing if hes not in the plasma or gone awol on us as we keep throwing smoke bombs at him ......but my point is the healing is not over the top.
We ran out of hypos trying differnt tactics a few runs back and our final attempt to nail the debuff info was all in melee range and .........well it went much faster than expected and we took much less damage. no one was stopping using abilities etc for the duration ( we were after all testing) and she went down like a cheap ho.
We have completed a few more times since and the Rebecca fight is now ...well its easy.
Word of warning though this may change after patch but definately 100% prior to todays patch the best (cough, legit, cough) way to defeat her (by defeat her i mean survive the debuff aoe)was all in melee range.