You will get one event with the unittag = "player" and a second one with the unittag "group1" assuming that group1 is the player. Both will return true to IsUnitPlayer(unitTag) obviously. You can either just use unittag == "player" to select only for those events.
If you want to have a more elegent version you can try to use AddfilterForEvent:
Lua Code:
EVENT_MANAGER:AddFilterForEvent([same as name as in your event declaration], EVENT_UNIT_DEATH_STATE_CHANGED, REGISTER_FILTER_UNIT_TAG , "player")
Then the event will only fire if the unittag matches "player". But I guess you usually won't get flooded with death events to a point where perfomance is an issue
Btw: This happens with all events where a target might have more then one unittag, also the unittags "reticleover", "reticleoverplayer" and "reticleovertarget" can cause similar issues.
PS: more on AddFilterForEvent is here:
http://wiki.esoui.com/AddFilterForEvent