Teysa, Opulant Oligarch currently will trigger multiple times if more than one clue is put into the graveyard at the same time and all triggers will successfully resolve and give a 1/1 spirit. Her ability should prevent all but the first trigger being put on the stack even if multiple instances of the trigger were to happen at once.

If it helps with bug testing, Delney being on the battlefield does not cause her to trigger additional times, it only happens due to multiple clues being destroyed at once.