The sentence is very confusing. I fully agree to that! :) A very nice question! +1
Pande would be in Mumbai on Monday, a day before Shah and Fadnavis, who is currently on a tour to the US, reaches the city.
'...a day before...' addresses Monday because it's talking about Tuesday.
'reaches the city...' talks about Fadanvis who's on the US tour.
The complexity happened because the author wanted to describe the coming of Shah and Fadanvis both BUT Shah is in India and Fadanvis is in the US.
Have a look...
I'll reach there on Monday, a day before you do.
You required 'do' there, a verb. Change it with a third person...
I'll reach there on Monday, a day before Mike does.
Replace the verb with the actual verb -reach.
I'll reach there on Monday, a day before Mike reaches.
Include one more person...
I'll reach there on Monday, a day before Jane and Mike reach (plural verb...because both are seen collectively as both of them are here!).
But then imagine that Mike is on the US tour! This'll separate the entities from each other.
I'll reach there on Monday, a day before Jane, and Mike, who is on the US tour reaches.
So, to answer your question...
Fadanvis (on the US tour) is reaching with Shah (who's in India) on Tuesday.
Pande is in India and already reached the city (Mumbai) today i.e. Monday.
Why the author uses 'would' in the very first sentence? Because the post is written before Monday!
How to write it without any ambiguity? Probably those cute parenthesis will help us a lot.
"Pande would be in Mumbai on Monday, a day before Fadanvis (who is currently on the US tour) and Shah reach the city."