Hi guys, I’m sorry to hear you feel the navigation is a bit weird. I can assure you we thought a lot about it and we built what we think is the best solution.
This is one of those cases where little trade-offs play a big part on a structural design decision. Here is my reasoning, open to discussion, as always 
Fact: TabBar and keyboard hate each other (let’s assume 99.99% of people don’t use a Bluetooth keyboard but the on-screen keyboard). Let’s focus also just on P2P payments since our chat is still plain off-the-shelf Intercom.
P2P relay heavily on the use of keyboard (you need to type amount, filter contacts, add a custom note, etc.) so, if we want to keep the TabBar visible these are our options:
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We don’t rise the keyboard automatically. Then the user needs an extra tap to click on the “Name or Phone Number” input. This happens a lot on Android. In other words, to avoid one tap for those that open the section indadvertedly we force users that actually want to send a payment to make always an extra tap.
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We don’t let you write on that first screen so there’s no need for keyboard. Either you choose a contact or you tap a “+” icon or similar. This is the pattern that WhatsApp and Telegram (and almost every other messenger app) follow. Since they have many conversations they can afford having a “menu” screen with a TabBar that always disappears when visiting a particular conversation. Then you have a “Back” in there. We may swift to this approach the moment we have more ways of sending and requesting money, but we’re not there yet.
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We do rise the keyboard and add some kind of “Hide keyboard” button that only acts as a way to reveal the TabBar again. Many (IMHO) poorly designed apps follow that pattern. It creates an extra in-between state that (again, IMHO) doesn’t make any sense. Even worse is when they don’t even give you a button but to hide the keyboard you need to tap on an empty area of the screen and such.
None of those options works for me. Maybe I’m missing something though.
Apart of that I always think on sending money as sending an email, a purely transitional UI that comes from the bottom of the screen, you deal with it and it disappears creating a new element on your feed (you can see the same pattern when creating alarms or contacts). I can imagine an app extension at some point to let you send payments from other apps, we may trigger personal payments from other parts of the app, etc. The pattern of bringing stuff from the bottom fits quite nicely (see every app that lets you send an email through a Mail app modal, it’s the same approach).
If you accept that last point you could argue that in that case “Send Money” shouldn’t be a TabBar element, and you’re right. That’s the trade-off. We’re treating an “action” as a “room” (the same that Instagram does with the camera) but we think it pays off. It’s either that or hide “Send Money” somewhere else.
Anyway, I can totally see where you come from (it was a tough sell internally too) but I hope the moment we have more stuff on the TabBar (probably 2 new sections at some point, “Recurring payments” and “Jars”) you’ll see that everything kind of make sense.
Sorry for such a long post, I should have recorded a podcast or something