Why didn't you continue on to work after the tire was repaired?
Even though they would have had your position somewhat (covered), they may have still needed you to finish the shift.
If nothing else, you could have given your explanation right then in real time while you were still dirty from fighting the tire. It would have demonstrated to your supes that you are a stand-up guy and you really want /need this job. You also wouldn't be worrying about the situation in the interim. Time to grow up son; this ain't high school anymore.
You can start a post, or a conversation, without using the lead-in (So) and it means exactly the same. It only serves to show a level of immaturity.