For your first question, you don’t need to click “I’ve Transferred…”. In fact, you don’t even need to go to the top-up screen. I’ve sent several top-ups to my Mondo card by simply going to my online banking and transferring the amount, including odd pence (e.g. £23.17). It eventually appears on my Mondo card and I get an alert when it does.
This isn’t as quick as topping up by debit card, though. Though the money presumably transfers to Mondo’s account within two hours (i.e. Faster Payment), it won’t appear on your card until Mondo has matched it to your account. I don’t know whether it’s done manually or if someone at Mondo runs a batch script, but it only happens on a working day. So if you sent a Faster Payments transfer now, it wouldn’t appear on your Mondo card until Tuesday morning (since Monday is a bank holiday). However, if you make a transfer on Wednesday morning, it should appear on your card that morning as well (since it’s within working hours).
Hope that makes sense. I don’t know if anyone from Mondo can shed light on what the reconciliation process is on their end (i.e. automated or someone manually looking through all their incoming amounts).