It wasn't clear in other reading that you couldn't use the same card. I'd planned to get one and add enough on it to cover planned bus, tram and metro rides plus the train. Guess not.
Actually yes, that's exactly what we did. We got a card, pre-loaded it with a certain amount of funds. It is good for metro, bus, train, tram and ferry. We used it for the trams, metro, and local trains (sintra, cascais).
I saw the same language that you did, which didn't make sense to me. I went to the ticket counter and made sure that the Viva Viagem card would also work for local trains.
Our Viva Viagem are mostly white, with some green with all 4 icons on the back. When we ran out of funds, we just went to a machine and loaded the additional amount that we needed. When you tap to use the metro, the machine will tell you your balance.
Just to note, they are not good for all trains. For example, when we traveled to Evora, we needed to buy separate tickets.
Edit to add: I'm thinking they are referencing when tourists commonly buy 24 hour passes for the metro, etc. In that case, you can't add a different fare type (zapping) until the 24 hours have passed.