Was Johnston supposed to be speaking in Mandarin all the time?

From the original script, it's not immediately clear. On the one hand, Johnston ("R.J.") is clearly fluent in Mandarin:

RJ stares at the faces which begin to peer in through the car windows. A grinning TWELVE YEAR-OLD slaps a poster against the glass.

R.J.(points at the ideogram on the poster) "China awake..."

and at the same time, the Emperor shows a strong understanding of written and spoken English:

Pu Yi points at a portrait on the cover of the Post — a special "Independence Day" issue.

PU YI: Who is this "George Washington"?

Since they can both communicate in each other's languages (and since the Emperor is eager to learn about the outside world) I'd imagine that they would speak English whenever possible.

Elsewhere in the Forbidden City, Mandarin would obviously be the lingua franca for general conversation.

When I was a child, my parents had bought this film on VHS in French. I can't quite recall what they were speaking throughout the movie, I'm currently watching it in English and it's so weird, it feels like they ought to be talking Chinese, and not just because they are Chinese (I should dig it up, but I think they were talking Mandarin with French subtitles). I do remember the character Reginald Johnson speaking English most of the time. So no, I think he was indeed supposed to be talking English. He was his tutor after all, so it would only make sense.