From the Stellar Developer Guide:
Each week, the protocol distributes these lumens to any account that gets over .05% of the “votes” from other accounts in the network.
What day of the week (and at what time) do these inflation payouts occur?
Inflation occurs when both of the following conditions occur:
The inflation round is computed as number of weeks since July 1st, 2014. So users can run inflation for the current round and all the previous rounds (if
inflation operation was not sent during the previous round).
If it's not time to run inflation the Stellar network will return
It depends on when somebody initiates it. From the same page you linked to:
Inflation is run in response to an inflation operation that anyone can submit to the network. This operation will fail if the inflation sequence number isn’t one after the last sequence number. It will also fail if (sequence number * 1 week) of time hasn’t elapsed since the network start date.
12am UTC on Tuesdays every week.
The other answers tell you how it works, but I felt it necessary to answer the actual question, of "What day of the week" by actually looking historically.
To properly answer your question, I had to do some digging in my related question: How can I determine when the last inflation was distributed?
I've gone back multiple inflation periods in the past couple months and they all have paid out at 12am UTC Tuesdays. For those in the US, that's Monday evening.
As of posting, the most recent inflation operations:
You'll notice that they've all been submitted by the same wallet, so it's safe to assume that the day/time will stay consistent for the foreseeable future.