Nepal was granted a TPS on 24th. TPS is given with the fact that it is not a favorable condition to go to Nepal due to the earthquake disaster. It does not matter whether a person has been living in US decades before or one day before 24th june, if that person has gone to Nepal after 24th June, USCIS might reject TPS for him, the reason being he felt comfortable to travel to Nepal. That's why USCIS wanted the continuous presence from 24th June, the day it granted TPS for Nepal.

As posted in so many earlier posts, you can have F1 and TPS side by side.