ZoteroBib in-text format is really the copy icon next to full cite
Just to be clear, because it does seem a little confusing. To get the in-text format you click the copy icon next to the full citation. If this is the case why don't you have some description to this effect (perhaps at top of the pop-up box with page omit author option). This would be a great help especially for children using the tool.
Also, I think this would be a very easy technical change to make.
Also, I think this would be a very easy technical change to make.
If you hover over that button, it says "Copy Citation" in the tooltip.
The popup box when you click on the button shows exactly what you're going to get in the clipboard, and the primary button says "Copy Citation".
The instructions at the bottom of the page show a large version of the same icon with an explanation of what it does: