Drain and refill, but do not flush it, and use Honda ATF only. As for the 4-3 downshift, The older generation Honda transmissions are notorious for abrubt downshifts (and generally rough shifting) even when in perfect mechanical health. A fluid drain and refill will smooth out the shifts a bit.

As for the new fluid causing failure, it can shock the system into failure if the fluid has never been changed since the car left the factory. If the rest of the car seems to have been well maintained, I would assume that the transmission has also been serviced... but of course you never know. I hope they had the timing belt replaced!

Not sure if it would help matters, but I suggest draining just a small amount first and refilling. Drive several miles, and then drain and refill again.

If it has never been changed, it won't go too much further anyway. Good luck.