Looking at other clubs using the same ticketing system. The digital ticket apparently will work with the previous game showing. If you click on show code it gives a barcode as backup if the nfc doesn't work. however to be safe i would just redownload your season ticket from the boro website.
From Brighton site
Your season ticket pass should update automatically to the next available fixture to you. This will only work if you have updates enabled in Google Wallet / Apple Wallet, for information on this, see the Apple/Android sections below. After updates have been enabled, it will update but this can take a while. Even if the wrong game is displayed, as long as you haven't shared, upgraded or moved you season ticket for the fixture, the pass will still work.