Regarding the card issuer, I did ask BigPay customer service by email

" Dear BigPay,
I like to know that sometime when I doing online transaction with debit / credit card, there is a column request for card issuing bank. What should I choose since BigPay is not a bank?
Regards"

This is the reply I got
"Hey Chai,

Noted on your enquiry. You must fill in the column for card issuer as "Tune Money Sdn Bhd or TPaay Asia Sdn Bhd". You can see the card issuer name printed behind your BIG PAY card.

Hope it is clarified!

Have a good day!

Regards,

DASA
The BigPay Team"

Hope that help.