Yes wearing a waistbelt over the waistcoat appears in many old images of people in Highland Dress. But to call it the only "proper" or "correct" way goes beyond the evidence I see.
As always, for a "reality check" I go back to The Highlanders of Scotland, for indeed that source is unique.
Of the figures which are wearing jackets and waistcoats, and the jacket is unbuttoned, I see:
16 men wearing no visible waistbelts
8 men wearing their waistbelt over both their jacket and waistcoat
2 men wearing waistbelts over the waistcoat
1 man wearing a waistbelt over his waistcoat but is jacketless
NONE of the waistcoats are tucked into the kilt, including the two men wearing waistbelts over their waistcoats. Here's one of them:
Also, NONE of the men are wearing waistbelts peaking out from under their waistcoats. This has always looked sloppy and "wrong" to me. It just wasn't done in the past... at least I don't recall coming across a vintage image of it.
Here's what it looks like:
Note how the black belt ruins the look of the shape of the bottom of the black waistcoat, foils the waistcoat's "line" and cut.
In a band, where you're stuggling to present uniformity, the waistbelts always fight against it, as they droop down to various level and are seen to various different degrees. How much better it looks, how much more uniform, and also how much more in line with tradtion it is to go without the belts:

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