Did Kakashi's sharingan evolve because Obito was watching?
Interesting question with no definite answer, so I'll post my 2c here.

The Mangekyou Sharingan is activated by the immense grief caused by killing the person closest to you. However, it seems like you don't actually have to kill him, but witnessing his death is enough.

For example, Itachi did not actually kill Shisui, rather, he watched him commit suicide (filler).

I believe that both of them awakened their Mangekyou Sharingans separately, and because they were both at the scene when it happened, it happened simultaneously.