As @jot's friend, member of Round 2.5 and Emily's other half I'll add: reimbursements took 2 days for us the first time and 1 day the second time. The first time it took about 20 days for the money to come back, the second time about 10 days.
The stories from Round 1 (e.g. @jot) scared the bejeezus out of us, we spent a solid Sunday getting every scrap of paper to prove our expenses (from invoice to credit card to bank account to our names on a bank statement proving ownership). They're more on top of the process now than in Round 1, we did have to get some extra docs but it just involved a few phone calls back home.
I believe for Round 3 it is a bit easier and I'd expect it to keep improving. Assume 1-2 days admin on this every month regardless (just with less follow-up stress after you submit your docs).
Such a drilldown is very helpful if you have applied and figuring things out. I thing the reimbursement process can be a little less cumbersome (from what it looks like from outside). I have applied too but I am not very excited about the said process.