please, it's urgent, who just recently change BVN phone number,

how long did it take?
how successful was it?

The staff at the bank told me that even if you change it, it won't reflect, so how true?

Yes, it won't reflect on your original database. I had same experience when I wanted to register for my NIN, I was told that my DOB is different from my original DOB. I guess the mistake was from the registerer. I rushed to my bank to make correction which they did but upon getting to NIN again thinking I had corrected the error, boom!!!! The error appeared on my NIN again. I complained but was told to go pay 15k to the Fg account through Remita and come back to NIMC in order to correct my DOB. I kukuma dey use the one wey dem do mistake.