Bad intonation up the neck could be attributed to needing a setup. It’s possible that the action is too high. Or the issue could be specific to the type of strings – some sets are thicker than others and sit too high in the nut slots which could pull a string to go sharp when fretted.
I just got a set of D’Addario titaniums and they are fat fluorocarbons that can be in tune in the open position but are immediately sharp when fretted (especially the C string, the fattest one). For reference, I’ve attached the D’Addario specs compared to Worth Browns.