Did Kakashi's sharingan evolve because Obito was watching? Both Kakashi and Obito awaken their Mangekyou at the same time as told in this question When did Kakashi and Obito awaken their Mangekyou Sharingan?  The sharingan Kakashi owns originally came from Obito, so is it due to Obito also being there at the moment Rin died that Kakashi's Mangekyou also awakend? Or asked in a different way. Would Kakashi have been able to awaken the Mangekyou without Obito being there?
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.