Hilariously, the physical cards can only be topped up at add fare machines (cash only) or ATMs (cash only).
If you go down the "add a pasmo/suica on your phone" then you get into licensing issues with the other cabal (credit card issuers): you need to use an Amex to charge it via Apple Pay (IIRC Visa is now supported, but when I tried it last week my card was declined, so... YMMV).