Arrival Lounge =/= First Class Lounge

On the day on which you arrive in First Class you can use the First Class Lounge upon arrival. It is open from 5:30 until 22:30.
The arrival Lounge is for LX Business Class, Freqent Traveler and Senator arrivals and only open from 6am to 1pm.

You will be able to use the First Class Lounge when arriving in ZRH, but the next day since your connection is in Business Class you will only be allowed to use the Business Class Lounge. (Or if you are *G, the Senator Lounge or the Alpin Café)

I agree that the recent change in the wording on the Swiss Lounge page could be interpreted to mean that you get F Lougne access on every segment of the ticket when it was booked in First, but historically that was never the case so I doubt they changed that. The wroding was only changed so that it was clear that you wouldn't get access to the FCL if your ticket didn't route through the airport in which the FCL is.