So this is where legal stuff gets complicated. Judges don't send the jury into deliberations with a copy of the revenant laws, but they write instructions that lay out the criteria the jury has to deliberate on. For simpler cases, it's a checklist of things, like for a DUI, "Was the defendant driving the vehicle?" "Was the defendant impaired?" and so on. For a murder case, it gets tricky. I don't have a way to view those instructions, so it's possible that the instructions basically laid it out as "If x and y and z, then you will find them guilty with a death sentence, however if x and y but not z, then they're guilty with a life imprisonment, and finally if not x or not y, then they're not guilty".

It's also possible that they did have a vote and voted to recommend a death sentence, however, it would still be entirely up to the judge to follow though with that recommendation. Jury sentencing guidelines are entirely non-binding. Judges are bound by the guidelines defined by the letter of the law and other cases.

We may never know if it was as black and white as them voting for "Execute or not" or if it was just the outcome of the jury instructions. Both cases are reasonable for a jury member to feel guilt over.