You can usually argue with them and get that fee waived. BUT, then they turn around and get you another way, such as reducing your credit line, or raising your interest. I’ve had them do this to me with on-line payments too — slap a late fee on me even though I’ve paid on time. Read your statement every time.
Quite a few don't credit on-line payments for several days, especially weekends, holidays. The advantage they used to have over phoned in payments was that there was no fee vs. a pretty high fee over the phone. I've noticed recently the phoned in payments for several no longer carry a fee and I believe are credited same day, as I have heard no disclaimers to the contrary. (I'm sure as heck no financial adviser, though, so be careful with any advice from me.)
Best practice is to close the credit accounts and pay cash. Dave Ramsey is right.