Seems interesting. Definitely would be great to have a solution to this. Does this require management to approve each expense? If so, it seems the next-day reimbursement is a pipe dream. If not, how do you with illegitimate expenses?
Sometimes managers worry that these notifications will get annoying (we worried about that too). What we've found is that managers actually like the transparency of knowing what their team is up to, and it's a great opportunity to send a little love to your employees by getting back to them quickly. It also takes just a few seconds / day. You can turn off the notifications, but most people don't.