2-gang switch with 3 black wires, how to wire up smart switches?

A friend and I have been wiring up my new home (built 2012, neutrals everywhere) with Lutron Caseta smart switches (specifically in this case, PDW-5ANS-WH-A) and he was working on my guest bathroom and took apart the old switches before I got a look… and then he called me in because he was stumped:

There are two single pole switches, one for the light and one for the fan.

There are two ground wires — one each.

There is several neutral wires capped with a wire nut, not attached to the original switches as has been standard — I just add the neutral from the Caseta to the bundle (upgrade the wire nut if needed) and that’s fine.

Then it gets weird: there are three left over black wires, not four. And there were wires directly between the two switches.

I ended up wiring the two red Lutron switches to one of them, and then the two black on the switches to one each of the remaining two.

I may have remembered that backwards, but regardless, it works, except that the light switch is now dependent on the fan switch. If the fan is off, the light switch doesn’t work. And if you turn on the fan, the light turns on (default Caseta behavior after loss of power I believe) and can be controlled, but as soon as you turn the fan off, it also goes off.

I don’t recall the original switches behaving that way, so is there a way to wire this so that they work independently?