I've had a CapitalOne 360 account since before CapitalOne bought out ING's ING Direct online banking division. It's one of the few places where you can physically deposit checks into your CapitalOne 360 online-only checking account. It's been useful to me a number of times, being able to actually go to someone to help me with the rare issue with my bank account rather than having to navigate a phone menu or escalation tree.
Even before the purchase, ING Direct was playing with the coffee shop-cum-bank concept.
The South End and Boylston Street locations feature meeting spaces that they donate to non-profits to reserve. If anything, they act as brand embassies to CapitalOne 360. They're not heavy-handed with selling you their banking products because they're already providing a casual atmosphere that also doubles as a means of brand exposure. I don't know the business relationship with Peet's Coffee and CapitalOne 360 - how they manage leasing of the space, who pays who to be in said space - but it probably doesn't hurt to partner/split the cost of business expansion with a large national bank.
The cafe in Ink Block is also very much an island in a way that the other Boston branches at Cleveland Circle, Boylston Street (formerly Anthrpopologie), and Downtown Crossing (Tremont & Winter Sts) aren't, so I'm not surprised to hear that it's dead at any hour on any day of the week. Google seems to think that one is more busy in the late morning than any other time.
Either way, it'll be a nice third space for people working here during the day. Depending on how much of the ground floor retail in Parcel H it'll be taking up, it could be adding more useful meeting space for non-profits and other groups now competing for space at District Hall across the street.
CapitalOne's full banks have also paired up with Starbucks elsewhere. I've camped out at this one on 42nd Street in Manhattan while I waited for a friend to interview with an architecture firm. The bank closed, a security partition went down, and it just turned into a Starbucks. It's possible they could do that here, too. Again, low risk venture for them while still achieving brand awareness with the general public and providing actual banking services to their customers.
I was an ING Direct account holder and after the acquisition I became a Capital One account holder (they just retired the 360 branding a month or so ago). I think the difference between Citi and Capital One is that Citi was an expansion into the area whereas because of ING Direct being an online bank, there were already thousands of account holders before they even set up a physical presence. I don't mind the café/bank setup and think it's a smart use of space compared to a boring bank, however, these cafes are only open during banking hours! So inconvenient. They should really use the café aspect to bring life to these storefronts when the bank is closed.